Exhibit 3.5 The following questions are based on this problem and accompanying Excel windows. A company is planning production for the next 4 quarters. They want to minimize the cost of production. The production cost is stable but demand and production capacity vary from quarter to quarter. The maximum amount of inventory which can be held is 12,000 units and management wants to keep at least 3,000 units on hand. Quarterly inventory holding cost is 3% of the cost of production. The company estimates the number of units carried in inventory each month by averaging the beginning and ending inventory for each month. There are currently 5,000 units in inventory. The company wants to produce at no less than one half of its maximum capacity in any quarter. $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Quarter }$ $\begin{array}{l} \begin{array} { l r r r r } & 1 & 2 & 3 & { 4 } \\ \hline \text { Unit Production Cost } & \$ 300 & \$ 300 & \$ 300 & \$ 300 \\ \text { Units Demanded } & 2,000 & 9,000 & 12,000 & 11,000 \\ \text { Maximum Production } & 8,000 & 7,000 & 8,000 & 9,000 \end{array} \end{array}$ \(\begin{array} { l l } \text { Let } & P _ { i } = \text { number of units produced in quarter } i , i = 1 , \ldots , 4 \\ & B _ { i } = \text { beginning inventory for quarter i } \\ \\ \text { MiN: } & 300 P _ { 1 } + 300 P _ { 2 } + 300 P _ { 3 } + 300 P _ { 4 } + \\ & 9 \left( B _ { 1 } + B _ { 2 } \right) / 2 + 9 \left( B _ { 2 } + B _ { 3 } \right) / 2 + 9 \left( B _ { 3 } + B _ { 4 } \right) / 2 + 9 \left( B _ { 4 } + B _ { 5 } \right) / 2 \\ \text { Subject to: } & 4000 \leq P _ { 1 } \leq 8000 \\ & 3500 \leq P _ { 2 } \leq 7000 \\ & 4000 \leq P _ { 3 } \leq 8000 \\ & 4500 \leq P _ { 4 } \leq 9000 \\ &3000 \leq B _ { 1 } + P _ { 1 } - 2000 \leq 12000 \\ & 3000 \leq B _ { 2 } + P _ { 2 } - 9000 \leq 12000 \\ &3000 \leq B _ { 3 } + P _ { 3 } - 12000 \leq 12000 \\ & 3000 \leq B _ { 4 } + P _ { 4 } - 11000 \leq 12000 \\ & B _ { 2 } = B _ { 1 } + P _ { 1 } - 2000 \\ & B _ { 3 } = B _ { 2 } + P _ { 2 } - 9000 \\ &B _ { 4 } = B _ { 3 } + P _ { 3 } - 12000 \\ & B _ { 5 } = B _ { 4 } + P _ { 4 } - 11000 \\ &P _ { i } , B _ { i } \geq 0 \end{array}\) \(\begin{array}{|c|l|c|c|c|c|c|} \hline &{\text { A }} & \mathrm{B} & \mathrm{C} & \mathrm{D} & \mathrm{E} & \mathrm{F} \\ \hline 1 & & & & \text { Quarter } & & \\ \hline 2 & & & 1 & 2 & 3 & 4 \\ \hline 3 & \text { Beginning Inventory } & & 5,000 & 11,000 & 9,000 & 5,000 \\ \hline 4 & \text { Units Produced } & & 8,000 & 7,000 & 8,000 & 9,000 \\ \hline 5 & \text { Units Demanded } & & 2,000 & 9,000 & 12,000 & 11,000 \\ \hline 6 & \text { Ending Inventory } & & 11,000 & 9,000 & 5,000 & 3,000 \\ \hline 7 & & & & & & \\ \hline 8 & \text { Minimum Procduction } & & 4,000 & 3,500 & 4,000 & 4,500 \\ \hline 9 & \text { Maximum Froduction } & & 8,000 & 7,000 & 8,000 & 9,000 \\ \hline 10 & & & & & & \\ \hline 11 & \text { Minimum Inventory } & & 3,000 & 3,000 & 3,000 & 3,000 \\ \hline 12 & \text { Maximum Inventory } & & 12,000 & 12,000 & 12,000 & 12,000 \\ \hline 13 & & & & & & \\ \hline 14 & \text { Unit Production Cost } & & \$ 300 & \$ 300 & \$ 300 & \$ 300 \\ \hline 15 & \text { Unit Carrying Cost } & 3.0 \% & \$ 9,00 & \$ 9.00 & \$ 9,00 & \$ 9.00 \\ \hline 16 & & & & & & \\ \hline 17 & \text { Quarterly Production Cost } & & \$ 2,400,000 & \$ 2,100,000 & \$ 2,400,000 & \$ 2,700,000 \\ \hline 18 & \text { Quarterly Carrying Cost } & & \$ 72,000 & \$ 90,000 & \$ 63,000 & \$ 36,000 \\ \hline 19 & & & & & & \\ \hline 20 & & & & & \text { Tota1 Cost } & \$ 9,861,000 \\ \hline \end{array}\) -Refer to Exhibit 3.5. What formula should be entered in cell C18 in the accompanying Excel spreadsheet to compute the quarterly carrying costs?

A) =C15*C3+C6 B) =C15*(C3+C6) C) =C15*C3/2 D) =C15*(C3+C6)/2 A) =C15*C3+C6 B) =C15*(C3+C6) C) =C15*C3/2 D) =C15*(C3+C6)/2

The hospital administrators at New Hope, County General, and City East recently received notice of an impending state inspection of their facilities. Under new guidelines established to improve the overall health care system, state inspectors will be assessing the efficiency of each hospital. The staff at New Hope has suggested a mutual assistance program in preparation for the inspections and have proposed using DEA as a means to assess the efficiency of each facility. The data collected thus far is summarized in the following table. All data reflects averages compiled over the past six months. $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Hospital}$ $\begin{array}{lccc} &\text { New Hope } &\text { County General }&\text {City East }\\ \hline \text {Input Measures}\\ \text { Bed days unused (1000s) } & 83.0 & 105.0 & 104.1 \\ \text { Supply expense }(\$ 1000 s) & 123.8 & 162.3 & 154.0 \\ \text { Full-time staff } & 225.0 & 200.0 & 231.0 \\ \text { Output Measures } & & & 82.7 \\ \text { Patient-days (1000s) } & 105.0 & 71.0 & 175.0 \\ \text { Nurses qualified } & 253.0 & 92.0 & 65.0 \\ \text { Assistants on staff } & 125.0 & 45.0 & 830 \end{array}$ Based on the following formulation, is City East efficient? If not, what input and output values should they aspire to in order to become efficient? Let $\quad w _ { i } =$ weight assigned to output $j , j = 1 , \ldots , 4$ $\mathbf { v } _ { i } =$ weight assigned to input $i , i = 1 , \ldots , 3$ MAX: $ \quad 82.7 w _ { 1 } + 175 .0 w _ { 2 } + 65.0 w _ { 3 } + 83 .0 w _ { 4 }$ Subject to: $105.1 w _ { 1 } + 253.0 w _ { 2} + 125.0 w _ { 3 } + 98.0 w _ { 4 } - 83.0 v _ { 1 } - 123.8 v _ { 2 } - 225.0 v _ { 3 } \leq 0$ $71.0 w _ { 1 } + 92.0 w _ { 2 } + 45.0 w _ { 3 } + 88.0 w _ { 4 } - 105.0 v _ { 1 } - 162.3 v _ { 2 } - 200 v _ { 3 } \leq 0$ $82.7 w _ { 1 } + 175.0 w _ { 2 } + 65.0 w _ { 3 } + 83.0 w _ { 4 } - 104.1 v _ { 1 } - 154.0 v _ { 2 } - 231.0 v _ { 3 } \leq 0$ $104.1 \mathbf { v } _ { 1 } + 154.0 \mathbf { v } _ { \mathbf { 2 } } + 231.0 \mathbf { v } _ { \mathbf { 3 } } = 1$ $w _ { 1 , } w _ { 2 } w _ { 3 , } w _ { 4 } , \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } \geq 0$

No, City East is not efficient. The foll

You have been given the following linear programming model and Excel spreadsheet to solve this problem. What formulas should be entered into cells E5 and D8:D10 to implement this model? \[\begin{array} { l l } \text { MAX: } & 2 X _ { 1 } + 7 X _ { 2 } \\ \text { Subject to: } & 5 X _ { 1 } + 9 X _ { 2 } \leq 90 \\ & 9 X _ { 1 } + 8 X _ { 2 } \leq 144 \\ & X _ { 2 } \leq 8 \\ & X _ { 1 } , X _ { 2 } \geq 0 \end{array}\] \[\begin{array} { | c | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\ \hline 1 & & & & & \\ \hline 2 & & & & & \\ \hline 3 & & \mathrm { X } _ { 1 } & \mathrm { X } _ { 2 } & & \\ \hline 4 & \text { Number to make: } & & & & \text { OBJ. FN. VALUE } \\ \hline 5 & \text { Unit profit: } & 2 & 7 & & \\ \hline 6 & & & & & \\ \hline 7 & \text { Constraints: } & & & \text { Used } & \text { Available } \\ \hline 8 & 1 & 5 & 9 & & 90 \\ \hline 9 & 2 & 9 & 8 & & 144 \\ \hline 10 & 3 & 0 & 1 & & 8 \\ \hline \end{array}\]

The answer of You have been given the following linear...

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. The following table summarizes the data for the problem. $\begin{array} { l | c c c c c } & \text { Profit per } & \text { Yield per } & \text { Maximum } & \text { Irrigation } &\text { Fertilizer }\\ \text { Crop } &\text { Acre(\$)}&\text { Acre (lb) } & \text { Demand (lb) } & \text { (acre ft) }&\text { (pounds/acre) }\\ \hline \text { Corn } & 2,100 & 21,000 & 20,000 & 2 & 500 \\ \text { pumpkin } & 900 & 10,000 & 180,000 & 3 & 400 \\ \text { Beans } & 1,050 & 3,500 & \text { Ba,000 } & 1 & 300 \end{array}$ What are the key formulas for this Excel spreadsheet implementation of the following formulation? $\begin{array} { ll } \text { Let }&\mathbf { X } _ { 1 } = \text { aces of carm } \\ &X _ { \mathbf { z } } = \operatorname { acres } \text { of punglan } \\ &\mathbf { X } _ { \mathbf { 3 } } = \text { acres of beans } \\ \text { MAX: }& \ 2100 X _ { 1 } + 900 X _ { 2 } + 1050 X _ { 3 } \\ \text { Subject to: } &21 X _ { 1 } \leq 200 \\ &10 \mathrm { X } _ { 2 } \leq 180 \\ &3.5 \mathrm { X } _ { 3 } \leq 80 \\ &2 X _ { 1 } + 3 X _ { \mathbf { 2 } } + 1 X _ { 3 } \leq 50 \\ &5 X _ { 1 } + 4 X _ { 2 } + 3 X _ { 3 } \leq 80 \\ &X _ { 1 } , X _ { 2 } X _ { 3 } \geq 0 \\ \end{array}$ \[\begin{array} { | c | c | c | c | c | c | c } \hline & { \mathrm { A } } & \mathrm { B } & \mathrm { C } & \mathrm { D } & \mathrm { E } & \mathrm { F } \\ \hline 1 & & \text { Farm } & \text { Plenning } & \text { Prablem } & & \\ \hline 2 & & & & & & \\ \hline 3 & & \text { Carn } & \text { Pumpkin } & \text { Benns } & & \\ \hline 4 & \text { Acres ta plant } & & & & & \text { Tatal Prafit: } \\ \hline 5 & \text { Prafit per acre } & 2100 & 900 & 1050 & & \\ \hline 6 & & & & & & \\ \hline 7 & \text { Constraints: } & & & & \text { Used } & \text { Available } \\ \hline 8 & \text { Corn denand } & 21000 & & & & \text { 200000 } \\ \hline 9 & \text { Pumpkin demand } & & 10000 & & & 180000 \\ \hline 10 & \text { Bean demand } & & & 3500 & & \text { 80000 } \\ \hline 11 & \text { Water } & 2 & 3 & 1 & & 50 \\ \hline 12 & \text { Fetilizer } & 500 & 400 & 300 & & 8000 \\ \hline \end{array}\]

The answer of A farmer is planning his spring planting....

Exhibit 3.5 The following questions are based on this problem and accompanying Excel windows. A company is planning production for the next 4 quarters. They want to minimize the cost of production. The production cost is stable but demand and production capacity vary from quarter to quarter. The maximum amount of inventory which can be held is 12,000 units and management wants to keep at least 3,000 units on hand. Quarterly inventory holding cost is 3% of the cost of production. The company estimates the number of units carried in inventory each month by averaging the beginning and ending inventory for each month. There are currently 5,000 units in inventory. The company wants to produce at no less than one half of its maximum capacity in any quarter. $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Quarter }$ $\begin{array}{l} \begin{array} { l r r r r } & 1 & 2 & 3 & { 4 } \\ \hline \text { Unit Production Cost } & \$ 300 & \$ 300 & \$ 300 & \$ 300 \\ \text { Units Demanded } & 2,000 & 9,000 & 12,000 & 11,000 \\ \text { Maximum Production } & 8,000 & 7,000 & 8,000 & 9,000 \end{array} \end{array}$ \(\begin{array} { l l } \text { Let } & P _ { i } = \text { number of units produced in quarter } i , i = 1 , \ldots , 4 \\ & B _ { i } = \text { beginning inventory for quarter i } \\ \\ \text { MiN: } & 300 P _ { 1 } + 300 P _ { 2 } + 300 P _ { 3 } + 300 P _ { 4 } + \\ & 9 \left( B _ { 1 } + B _ { 2 } \right) / 2 + 9 \left( B _ { 2 } + B _ { 3 } \right) / 2 + 9 \left( B _ { 3 } + B _ { 4 } \right) / 2 + 9 \left( B _ { 4 } + B _ { 5 } \right) / 2 \\ \text { Subject to: } & 4000 \leq P _ { 1 } \leq 8000 \\ & 3500 \leq P _ { 2 } \leq 7000 \\ & 4000 \leq P _ { 3 } \leq 8000 \\ & 4500 \leq P _ { 4 } \leq 9000 \\ &3000 \leq B _ { 1 } + P _ { 1 } - 2000 \leq 12000 \\ & 3000 \leq B _ { 2 } + P _ { 2 } - 9000 \leq 12000 \\ &3000 \leq B _ { 3 } + P _ { 3 } - 12000 \leq 12000 \\ & 3000 \leq B _ { 4 } + P _ { 4 } - 11000 \leq 12000 \\ & B _ { 2 } = B _ { 1 } + P _ { 1 } - 2000 \\ & B _ { 3 } = B _ { 2 } + P _ { 2 } - 9000 \\ &B _ { 4 } = B _ { 3 } + P _ { 3 } - 12000 \\ & B _ { 5 } = B _ { 4 } + P _ { 4 } - 11000 \\ &P _ { i } , B _ { i } \geq 0 \end{array}\) \(\begin{array}{|c|l|c|c|c|c|c|} \hline &{\text { A }} & \mathrm{B} & \mathrm{C} & \mathrm{D} & \mathrm{E} & \mathrm{F} \\ \hline 1 & & & & \text { Quarter } & & \\ \hline 2 & & & 1 & 2 & 3 & 4 \\ \hline 3 & \text { Beginning Inventory } & & 5,000 & 11,000 & 9,000 & 5,000 \\ \hline 4 & \text { Units Produced } & & 8,000 & 7,000 & 8,000 & 9,000 \\ \hline 5 & \text { Units Demanded } & & 2,000 & 9,000 & 12,000 & 11,000 \\ \hline 6 & \text { Ending Inventory } & & 11,000 & 9,000 & 5,000 & 3,000 \\ \hline 7 & & & & & & \\ \hline 8 & \text { Minimum Procduction } & & 4,000 & 3,500 & 4,000 & 4,500 \\ \hline 9 & \text { Maximum Froduction } & & 8,000 & 7,000 & 8,000 & 9,000 \\ \hline 10 & & & & & & \\ \hline 11 & \text { Minimum Inventory } & & 3,000 & 3,000 & 3,000 & 3,000 \\ \hline 12 & \text { Maximum Inventory } & & 12,000 & 12,000 & 12,000 & 12,000 \\ \hline 13 & & & & & & \\ \hline 14 & \text { Unit Production Cost } & & \$ 300 & \$ 300 & \$ 300 & \$ 300 \\ \hline 15 & \text { Unit Carrying Cost } & 3.0 \% & \$ 9,00 & \$ 9.00 & \$ 9,00 & \$ 9.00 \\ \hline 16 & & & & & & \\ \hline 17 & \text { Quarterly Production Cost } & & \$ 2,400,000 & \$ 2,100,000 & \$ 2,400,000 & \$ 2,700,000 \\ \hline 18 & \text { Quarterly Carrying Cost } & & \$ 72,000 & \$ 90,000 & \$ 63,000 & \$ 36,000 \\ \hline 19 & & & & & & \\ \hline 20 & & & & & \text { Tota1 Cost } & \$ 9,861,000 \\ \hline \end{array}\) -Refer to Exhibit 3.5. Which cells are changing cells in the accompanying Excel spreadsheet?

A) C4:F4 B) C9:F9 C) F20 D) C12:F12 A) C4:F4 B) C9:F9 C) F20 D) C12:F12

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. There are only 50 acre ft of irrigation available and only 8,000 pounds/acre of fertilizer available. The following table summarizes the data for the problem. \[\begin{array} { l | c c c c c } \text { Crop } & \begin{array} { c } \text { Profit per } \\ \text { Acre } ( \$ ) \end{array} & \begin{array} { c } \text { Yield per } \\ \text { Acre (Ib) } \end{array} & \begin{array} { c } \text { Maximum } \\ \text { Demand (Ib) } \end{array} & \begin{array} { c } \text { Irrigation } \\ \text { (acre ft) } \end{array} & \begin{array} { c } \text { Fertilizer } \\ \text { (pounds/acre) } \end{array} \\ \hline \text { Corn } & 2,100 & 21,000 & 200,000 & 2 & 500 \\ \text { Pumpkin } & 900 & 10,000 & 180,000 & 3 & 400 \\ \text { Beans } & 1,050 & 3,500 & 80,000 & 1 & 300 \end{array}\] Formulate the LP for this problem.

The answer of A farmer is planning his spring planting....

The constraints X1 $\ge$ 0 and X2$\ge$ 0 are referred to as

A) positivity constraints. B) optimality conditions. C) left hand sides. D) nonnegativity conditions. A) positivity constraints. B) optimality conditions. C) left hand sides. D) nonnegativity conditions.

You have been given the following linear programming model and Excel spreadsheet to solve this problem. What numbers should be entered into cells B5:C5 and B8:C10 to implement this model? \[\begin{array} { l l } \text { MAX: } & 2 X _ { 1 } + 7 X _ { 2 } \\ \text { Subject to: } & 5 X _ { 1 } + 9 X _ { 2 } \leq 90 \\ & 9 X _ { 1 } + 8 X _ { 2 } \leq 144 \\ & X _ { 2 } \leq 8 \\ & X _ { 1 } , X _ { 2 } \geq 0 \end{array}\] \[\begin{array} { | c | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\ \hline 1 & & & & & \\ \hline 2 & & & & & \\ \hline 3 & & X _ { 1 } & \mathrm { X } _ { 2 } & & \\ \hline 4 & \text { Number to make: } & & & & \text { OBJ. FN. VALUE } \\ \hline 5 & \text { Unit profit: } & & & & \\ \hline 6 & & & & & \\ \hline 7 & \text { Constraints: } & & & \text { Used } & \text { Available } \\ \hline 8 & 1 & & & & 90 \\ \hline 9 & 2 & & & & 144 \\ \hline 10 & 3 & & & & 8 \\ \hline \end{array}\]

The answer of You have been given the following linear...

Exam 3: Modeling and Solving Lp Problems in a Spreadsheet

Exhibit 3.5 The following questions are based on this problem and accompanying Excel windows. A company is planning production for the next 4 quarters. They want to minimize the cost of production. The production cost is stable but demand and production capacity vary from quarter to quarter. The maximum amount of inventory which can be held is 12,000 units and management wants to keep at least 3,000 units on hand. Quarterly inventory holding cost is 3% of the cost of production. The company estimates the number of units carried in inventory each month by averaging the beginning and ending inventory for each month. There are currently 5,000 units in inventory. The company wants to produce at no less than one half of its maximum capacity in any quarter. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\text { Quarter }$ 1 2 3 4 Unit Production Cost \ 300 \ 300 \ 300 \ 300 Units Demanded 2,000 9,000 12,000 11,000 Maximum Production 8,000 7,000 8,000 9,000 Let = number of units produced in quarter i,i=1,\ldots,4 = beginning inventory for quarter i MiN: 300+300+300+300+ 9 + /2+9 + /2+9 + /2+9 + /2 Subject to: 4000\leq\leq8000 3500\leq\leq7000 4000\leq\leq8000 4500\leq\leq9000 3000\leq+-2000\leq12000 3000\leq+-9000\leq12000 3000\leq+-12000\leq12000 3000\leq+-11000\leq12000 =+-2000 =+-9000 =+-12000 =+-11000 ,\geq0 A 1 Quarter 2 1 2 3 4 3 Beginning Inventory 5,000 11,000 9,000 5,000 4 Units Produced 8,000 7,000 8,000 9,000 5 Units Demanded 2,000 9,000 12,000 11,000 6 Ending Inventory 11,000 9,000 5,000 3,000 7 8 Minimum Procduction 4,000 3,500 4,000 4,500 9 Maximum Froduction 8,000 7,000 8,000 9,000 10 11 Minimum Inventory 3,000 3,000 3,000 3,000 12 Maximum Inventory 12,000 12,000 12,000 12,000 13 14 Unit Production Cost \ 300 \ 300 \ 300 \ 300 15 Unit Carrying Cost 3.0\% \ 9,00 \ 9.00 \ 9,00 \ 9.00 16 17 Quarterly Production Cost \ 2,400,000 \ 2,100,000 \ 2,400,000 \ 2,700,000 18 Quarterly Carrying Cost \ 72,000 \ 90,000 \ 63,000 \ 36,000 19 20 Tota1 Cost \ 9,861,000 -Refer to Exhibit 3.5. What formula should be entered in cell C18 in the accompanying Excel spreadsheet to compute the quarterly carrying costs?

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Question 41

The hospital administrators at New Hope, County General, and City East recently received notice of an impending state inspection of their facilities. Under new guidelines established to improve the overall health care system, state inspectors will be assessing the efficiency of each hospital. The staff at New Hope has suggested a mutual assistance program in preparation for the inspections and have proposed using DEA as a means to assess the efficiency of each facility. The data collected thus far is summarized in the following table. All data reflects averages compiled over the past six months. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\text { Hospital}$ New Hope County General City East Input Measures Bed days unused (1000s) 83.0 105.0 104.1 Supply expense (\ 1000s) 123.8 162.3 154.0 Full-time staff 225.0 200.0 231.0 Output Measures 82.7 Patient-days (1000s) 105.0 71.0 175.0 Nurses qualified 253.0 92.0 65.0 Assistants on staff 125.0 45.0 830 Based on the following formulation, is City East efficient? If not, what input and output values should they aspire to in order to become efficient? Let $\quad w _ { i } =$ weight assigned to output $j , j = 1 , \ldots , 4$ $\mathbf { v } _ { i } =$ weight assigned to input $i , i = 1 , \ldots , 3$ MAX: $\quad 82.7 w _ { 1 } + 175 .0 w _ { 2 } + 65.0 w _ { 3 } + 83 .0 w _ { 4 }$ Subject to: $105.1 w _ { 1 } + 253.0 w _ { 2} + 125.0 w _ { 3 } + 98.0 w _ { 4 } - 83.0 v _ { 1 } - 123.8 v _ { 2 } - 225.0 v _ { 3 } \leq 0$ $71.0 w _ { 1 } + 92.0 w _ { 2 } + 45.0 w _ { 3 } + 88.0 w _ { 4 } - 105.0 v _ { 1 } - 162.3 v _ { 2 } - 200 v _ { 3 } \leq 0$ $82.7 w _ { 1 } + 175.0 w _ { 2 } + 65.0 w _ { 3 } + 83.0 w _ { 4 } - 104.1 v _ { 1 } - 154.0 v _ { 2 } - 231.0 v _ { 3 } \leq 0$ $104.1 \mathbf { v } _ { 1 } + 154.0 \mathbf { v } _ { \mathbf { 2 } } + 231.0 \mathbf { v } _ { \mathbf { 3 } } = 1$ $w _ { 1 , } w _ { 2 } w _ { 3 , } w _ { 4 } , \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } \geq 0$

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Question 42

Exhibit 3.2 The following questions are based on this problem and accompanying Excel windows. The Byte computer company produces two models of computers, Plain and Fancy. It wants to plan how many computers to produce next month to maximize profits. Producing these computers requires wiring, assembly and inspection time. Each computer produces a certain level of profits but faces only a limited demand. There are also a limited number of wiring, assembly and inspection hours available in each month. The data for this problem is summarized in the following table. $\begin{array} { l c c c c c } &&\text { Maximum } &&\text { Assembly }&\text { Inspection } \\\text { Computer } &\text { Profit per }&\text { demand for }&\text { Wiring Hours } &\text { Hours } &\text { Hours } \\\text { Model }&\text { Model (\$)}&\text { product }&\text { Required }&\text { Required }&\text { Required }\\\hline \text { Plain } & 30 & 80 & .4 & .5 & .2 \\\text { Fancy } & 40 & 90 & .5 & .4 & .3 \\\hline & & \text { Hours Available } & 50 & 50 & 22\end{array}$ Let $\quad X _ { 1 } =$ Number of Plain computers to produce $\quad\quad X _ { 2 } =$ Number of Fancy computers to produce MAX: $\quad \quad\quad30 X _ { 1 } + 40 X _ { 2 }$ Subject to: $\quad .4 \mathrm { X } _ { 1 } + .5 \mathrm { X } _ { 2 } \leq 50$ (wiring hours) $\quad\quad\quad\quad\quad.5 \mathrm { X } _ { 1 } + .4 \mathrm { X } _ { 2 } \leq 50$ (assembly hours) $\quad\quad\quad\quad\quad.2 \mathrm { X } _ { 1 } + .2 \mathrm { X } _ { 2 } \leq 22$ (inspection hours) $\quad\quad\quad\quad\quad\mathrm { X } _ { 1 } \leq 80$ (Plin computers demand) $\quad\quad\quad\quad\quad\mathrm { X } _ { 2 } \leq 90$ (Fancy computers demand) $\quad\quad\quad\quad \quad X _ { 1 } , X _ { 2 } \geq 0$ A B C D E 1 Byte Computer Company 2 3 Plain Fancy 4 Number to make: Total Profit: 5 Unit profit: 30 40 6 7 Constraints: Used Available 8 Wiring 0.4 0.5 50 9 Assembly 0.5 0.4 50 10 Inspection 0.2 0.3 22 11 Plain Demand 1 80 12 Fancy Demand 1 90 -Refer to Exhibit 3.2. Which cells should be changing cells in this problem?

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Question 43

You have been given the following linear programming model and Excel spreadsheet to solve this problem. What formulas should be entered into cells E5 and D8:D10 to implement this model? MAX: 2+7 Subject to: 5+9\leq90 9+8\leq144 \leq8 ,\geq0 A B C D E 1 2 3 4 Number to make: OBJ. FN. VALUE 5 Unit profit: 2 7 6 7 Constraints: Used Available 8 1 5 9 90 9 2 9 8 144 10 3 0 1 8

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Question 44

Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons): Week Trucking Limits Railway Limits Air Cargo Limits 1 45 60 15 2 50 55 10 3 55 45 5 Costs (\ per 1000 tons) \ 200 \ 140 \ 400 The following is the LP model for this logistics problem. $Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons): \begin{array}{cccc} \text { Week } & \text { Trucking Limits } & \text { Railway Limits } & \text { Air Cargo Limits } \\ \hline 1 & 45 & 60 & 15 \\ 2 & 50 & 55 & 10 \\ 3 & 55 & 45 & 5 \\ \hline \text { Costs (\$ per } 1000 \text { tons) } & \$ 200 & \$ 140 & \$ 400 \end{array} The following is the LP model for this logistics problem. What values would you enter in the Risk Solver Platform (RSP) task pane for the cells in this Excel spreadsheet implementation of this problem? Objective Cell: Variables Cells: Constraints Cells:$ $Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons): \begin{array}{cccc} \text { Week } & \text { Trucking Limits } & \text { Railway Limits } & \text { Air Cargo Limits } \\ \hline 1 & 45 & 60 & 15 \\ 2 & 50 & 55 & 10 \\ 3 & 55 & 45 & 5 \\ \hline \text { Costs (\$ per } 1000 \text { tons) } & \$ 200 & \$ 140 & \$ 400 \end{array} The following is the LP model for this logistics problem. What values would you enter in the Risk Solver Platform (RSP) task pane for the cells in this Excel spreadsheet implementation of this problem? Objective Cell: Variables Cells: Constraints Cells:$ What values would you enter in the Risk Solver Platform (RSP) task pane for the cells in this Excel spreadsheet implementation of this problem? Objective Cell: Variables Cells: Constraints Cells:

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Question 45

A financial planner wants to design a portfolio of investments for a client. The client has $400,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 30% of the money in any one investment, at least one half should be invested in long-term bonds which mature in six or more years, and no more than 40% of the total money should be invested in B or C since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio. Investment Return Years to Maturity Rating 6.45\% 6 1-Excellent B 8.5\% 5 3-Gaod C 9.00\% 8 4-Fair D 7.75\% 4 2-Very Gaod Let = Dollars invested in = Dollars invested in = Dollars invested in = Dollars invested in MAX: Subject to: 45+.085+ . 990+.075 +++\leq400000 \leq120000 \leq120000 \leq120000 \leq120000 +\geq200000 +\leq160000 \geq0 $A financial planner wants to design a portfolio of investments for a client. The client has $400,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 30% of the money in any one investment, at least one half should be invested in long-term bonds which mature in six or more years, and no more than 40% of the total money should be invested in B or C since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio. \begin{array} { c c c l } \text { Investment } & \text { Return } & \text { Years to Maturity } & \text { Rating } \\ \hline \mathbf { A } & 6.45 \% & 6 & \text { 1-Excellent } \\ \text { B } & 8.5 \% & 5 & \text { 3-Gaod } \\ \text { C } & 9.00 \% & 8 & \text { 4-Fair } \\ \text { D } & 7.75 \% & 4 & \text { 2-Very Gaod } \end{array} \begin{array} { l l } \text { Let } & \mathbf { X } _ { 1 } = \text { Dollars invested in } \mathrm { A } \\ & \mathbf { X } _ { \mathbf { 2 } } = \text { Dollars invested in } \mathrm { B } \\ & \mathbf { X } _ { \mathbf { 3 } } = \text { Dollars invested in } \mathrm { C } \\ & \mathbf { X } _ { 4 } = \text { Dollars invested in } \mathrm { D } \\ \text { MAX: } & \\ \text { Subject to: } & \mathbf { X } 45 \mathbf { X } _ { 1 } + .085 \mathbf { X } _ { \mathbf { 2 } } + \text {. } 990 \mathbf { X } _ { \mathbf { 3 } } + .075 \mathbf { X } _ { 4 } \\ & \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } + \mathbf { X } _ { \mathbf { 3 } } + \mathbf { X } _ { 4 } \leq 400000 \\ & \mathbf { X } _ { 1 } \leq 120000 \\ & \mathbf { X } _ { \mathbf { 2 } } \leq 120000 \\ & \mathbf { X } _ { 3 } \leq 120000 \\ & \mathbf { X } _ { 4 } \leq 120000 \\ & \mathbf { X } _ { 1 } + \mathbf { X } _ { 3 } \geq 200000 \\ & \mathbf { X } _ { \mathbf { 2 } } + \mathbf { X } _ { 3 } \leq 160000 \\ & \mathbf { X } _ { 1 } \mathbf { X } _ { \mathbf { 2 } } \mathbf { X } _ { \mathbf { 3 } } \mathbf { X } _ { 4 } \geq 0 \end{array} What values would you enter in the Risk Solver Platform (RSP) task pane for the following cells for this Excel spreadsheet implementation of this problem? Objective Cell: Variables Cells: Constraints Cells:$ $A financial planner wants to design a portfolio of investments for a client. The client has $400,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 30% of the money in any one investment, at least one half should be invested in long-term bonds which mature in six or more years, and no more than 40% of the total money should be invested in B or C since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio. \begin{array} { c c c l } \text { Investment } & \text { Return } & \text { Years to Maturity } & \text { Rating } \\ \hline \mathbf { A } & 6.45 \% & 6 & \text { 1-Excellent } \\ \text { B } & 8.5 \% & 5 & \text { 3-Gaod } \\ \text { C } & 9.00 \% & 8 & \text { 4-Fair } \\ \text { D } & 7.75 \% & 4 & \text { 2-Very Gaod } \end{array} \begin{array} { l l } \text { Let } & \mathbf { X } _ { 1 } = \text { Dollars invested in } \mathrm { A } \\ & \mathbf { X } _ { \mathbf { 2 } } = \text { Dollars invested in } \mathrm { B } \\ & \mathbf { X } _ { \mathbf { 3 } } = \text { Dollars invested in } \mathrm { C } \\ & \mathbf { X } _ { 4 } = \text { Dollars invested in } \mathrm { D } \\ \text { MAX: } & \\ \text { Subject to: } & \mathbf { X } 45 \mathbf { X } _ { 1 } + .085 \mathbf { X } _ { \mathbf { 2 } } + \text {. } 990 \mathbf { X } _ { \mathbf { 3 } } + .075 \mathbf { X } _ { 4 } \\ & \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } + \mathbf { X } _ { \mathbf { 3 } } + \mathbf { X } _ { 4 } \leq 400000 \\ & \mathbf { X } _ { 1 } \leq 120000 \\ & \mathbf { X } _ { \mathbf { 2 } } \leq 120000 \\ & \mathbf { X } _ { 3 } \leq 120000 \\ & \mathbf { X } _ { 4 } \leq 120000 \\ & \mathbf { X } _ { 1 } + \mathbf { X } _ { 3 } \geq 200000 \\ & \mathbf { X } _ { \mathbf { 2 } } + \mathbf { X } _ { 3 } \leq 160000 \\ & \mathbf { X } _ { 1 } \mathbf { X } _ { \mathbf { 2 } } \mathbf { X } _ { \mathbf { 3 } } \mathbf { X } _ { 4 } \geq 0 \end{array} What values would you enter in the Risk Solver Platform (RSP) task pane for the following cells for this Excel spreadsheet implementation of this problem? Objective Cell: Variables Cells: Constraints Cells:$ What values would you enter in the Risk Solver Platform (RSP) task pane for the following cells for this Excel spreadsheet implementation of this problem? Objective Cell: Variables Cells: Constraints Cells:

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Question 46

Which type of spreadsheet cell represents the objective function in an LP model?

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Question 47

Exhibit 3.4 The following questions are based on this problem and accompanying Excel windows. A financial planner wants to design a portfolio of investments for a client. The client has $300,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 25% of the money in any one investment, at least one third should be invested in long-term bonds which mature in seven or more years, and no more than 25% of the total money should be invested in C or D since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio. Investment Return Years to Maturity Rating A 6.45\% 9 1-Excellent B 7.10\% 8 2 -Very Good C 8.20\% 5 4 -Fair D 9.00\% 8 3 -Good Let = Dollars invested in A = Dollars invested in B = Dollars invested in C = Dollars invested in D MAX: $\quad .0645 \mathrm { X } _ { 1 } + .071 \mathrm { X } _ { 2 } + .082 \mathrm { X } _ { 3 } + .09 \mathrm { X } _ { 4 }$ Subject to: +++\leq300000 \leq75000 \leq75000 \leq75000 \leq75000 ++\geq100000 +\leq75000 ,,\geq0 $Exhibit 3.4 The following questions are based on this problem and accompanying Excel windows. A financial planner wants to design a portfolio of investments for a client. The client has $300,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 25% of the money in any one investment, at least one third should be invested in long-term bonds which mature in seven or more years, and no more than 25% of the total money should be invested in C or D since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio. \begin{array} { c c c l } \text { Investment } & \text { Return } & \text { Years to Maturity } & \text { Rating } \\ \hline \text { A } & 6.45 \% & 9 & \text { 1-Excellent } \\ \text { B } & 7.10 \% & 8 & 2 \text { -Very Good } \\ \text { C } & 8.20 \% & 5 & 4 \text {-Fair } \\ \text { D } & 9.00 \% & 8 & 3 \text {-Good } \end{array} Let \begin{array} { l } X _ { 1 } = \text { Dollars invested in } A \\ X _ { 2 } = \text { Dollars invested in } B \\ X _ { 3 } = \text { Dollars invested in } C \\ X _ { 4 } = \text { Dollars invested in } D \end{array} MAX: \quad .0645 \mathrm { X } _ { 1 } + .071 \mathrm { X } _ { 2 } + .082 \mathrm { X } _ { 3 } + .09 \mathrm { X } _ { 4 } Subject to: \begin{array} { l } \mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } + \mathrm { X } _ { 3 } + \mathrm { X } _ { 4 } \leq 300000 \\ \mathrm { X } _ { 1 } \leq 75000 \\ \mathrm { X } _ { 2 } \leq 75000 \\ \mathrm { X } _ { 3 } \leq 75000 \\ \mathrm { X } _ { 4 } \leq 75000 \\ \mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } + \mathrm { X } _ { 4 } \geq 100000 \\ \mathrm { X } _ { 3 } + \mathrm { X } _ { 4 } \leq 75000 \\ \mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } , \mathrm { X } _ { 3 } \mathrm { X } _ { 4 } \geq 0 \end{array} -Refer to Exhibit 3.4. What formula should be entered in cell B7 in the accompanying Excel spreadsheet to compute total dollars invested?$ $Exhibit 3.4 The following questions are based on this problem and accompanying Excel windows. A financial planner wants to design a portfolio of investments for a client. The client has $300,000 to invest and the planner has identified four investment options for the money. The following requirements have been placed on the planner. No more than 25% of the money in any one investment, at least one third should be invested in long-term bonds which mature in seven or more years, and no more than 25% of the total money should be invested in C or D since they are riskier investments. The planner has developed the following LP model based on the data in this table and the requirements of the client. The objective is to maximize the total return of the portfolio. \begin{array} { c c c l } \text { Investment } & \text { Return } & \text { Years to Maturity } & \text { Rating } \\ \hline \text { A } & 6.45 \% & 9 & \text { 1-Excellent } \\ \text { B } & 7.10 \% & 8 & 2 \text { -Very Good } \\ \text { C } & 8.20 \% & 5 & 4 \text {-Fair } \\ \text { D } & 9.00 \% & 8 & 3 \text {-Good } \end{array} Let \begin{array} { l } X _ { 1 } = \text { Dollars invested in } A \\ X _ { 2 } = \text { Dollars invested in } B \\ X _ { 3 } = \text { Dollars invested in } C \\ X _ { 4 } = \text { Dollars invested in } D \end{array} MAX: \quad .0645 \mathrm { X } _ { 1 } + .071 \mathrm { X } _ { 2 } + .082 \mathrm { X } _ { 3 } + .09 \mathrm { X } _ { 4 } Subject to: \begin{array} { l } \mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } + \mathrm { X } _ { 3 } + \mathrm { X } _ { 4 } \leq 300000 \\ \mathrm { X } _ { 1 } \leq 75000 \\ \mathrm { X } _ { 2 } \leq 75000 \\ \mathrm { X } _ { 3 } \leq 75000 \\ \mathrm { X } _ { 4 } \leq 75000 \\ \mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } + \mathrm { X } _ { 4 } \geq 100000 \\ \mathrm { X } _ { 3 } + \mathrm { X } _ { 4 } \leq 75000 \\ \mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } , \mathrm { X } _ { 3 } \mathrm { X } _ { 4 } \geq 0 \end{array} -Refer to Exhibit 3.4. What formula should be entered in cell B7 in the accompanying Excel spreadsheet to compute total dollars invested?$ -Refer to Exhibit 3.4. What formula should be entered in cell B7 in the accompanying Excel spreadsheet to compute total dollars invested?

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Question 48

Exhibit 3.2 The following questions are based on this problem and accompanying Excel windows. The Byte computer company produces two models of computers, Plain and Fancy. It wants to plan how many computers to produce next month to maximize profits. Producing these computers requires wiring, assembly and inspection time. Each computer produces a certain level of profits but faces only a limited demand. There are also a limited number of wiring, assembly and inspection hours available in each month. The data for this problem is summarized in the following table. $\begin{array} { l c c c c c } &&\text { Maximum } &&\text { Assembly }&\text { Inspection } \\\text { Computer } &\text { Profit per }&\text { demand for }&\text { Wiring Hours } &\text { Hours } &\text { Hours } \\\text { Model }&\text { Model (\$)}&\text { product }&\text { Required }&\text { Required }&\text { Required }\\\hline \text { Plain } & 30 & 80 & .4 & .5 & .2 \\\text { Fancy } & 40 & 90 & .5 & .4 & .3 \\\hline & & \text { Hours Available } & 50 & 50 & 22\end{array}$ Let $\quad X _ { 1 } =$ Number of Plain computers to produce $\quad\quad X _ { 2 } =$ Number of Fancy computers to produce MAX: $\quad \quad\quad30 X _ { 1 } + 40 X _ { 2 }$ Subject to: $\quad .4 \mathrm { X } _ { 1 } + .5 \mathrm { X } _ { 2 } \leq 50$ (wiring hours) $\quad\quad\quad\quad\quad.5 \mathrm { X } _ { 1 } + .4 \mathrm { X } _ { 2 } \leq 50$ (assembly hours) $\quad\quad\quad\quad\quad.2 \mathrm { X } _ { 1 } + .2 \mathrm { X } _ { 2 } \leq 22$ (inspection hours) $\quad\quad\quad\quad\quad\mathrm { X } _ { 1 } \leq 80$ (Plin computers demand) $\quad\quad\quad\quad\quad\mathrm { X } _ { 2 } \leq 90$ (Fancy computers demand) $\quad\quad\quad\quad \quad X _ { 1 } , X _ { 2 } \geq 0$ A B C D E 1 Byte Computer Company 2 3 Plain Fancy 4 Number to make: Total Profit: 5 Unit profit: 30 40 6 7 Constraints: Used Available 8 Wiring 0.4 0.5 50 9 Assembly 0.5 0.4 50 10 Inspection 0.2 0.3 22 11 Plain Demand 1 80 12 Fancy Demand 1 90 -Refer to Exhibit 3.2. What formula should be entered in cell D8 in the accompanying Excel spreadsheet to compute the amount of wiring used?

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Question 49

Exhibit 3.3 The following questions are based on this problem and accompanying Excel windows. Jack's distillery blends scotches for local bars and saloons. One of his customers has requested a special blend of scotch targeted as a bar scotch. The customer wants the blend to involve two scotch products, call them A and B. Product A is a higher quality scotch while product B is a cheaper brand. The customer wants to make the claim the blend is closer to high quality than the alternative. The customer wants 50 1500 ml bottles of the blend. Each bottle must contain at least 48% of Product A and at least 500 ml of B. The customer also specified that the blend have an alcohol content of at least 85%. Product A contains 95% alcohol while product B contains 78%. The blend is sold for $12.50 per bottle. Product A costs $7 per liter and product B costs $3 per liter. The company wants to determine the blend that will meet the customer's requirements and maximize profit. Let $\quad X _ { 1 } =$ Number of liters of product $A _ { 1 }$ in total blend delivered $\quad\quad\quad\mathrm { X } _ { 2 } =$ Number of liters of product $\mathrm { B }$ in total blend delivered MIN: $\quad 7 \mathrm { X } _ { 1 } + 3 \mathrm { X } _ { 2 }$ Subject to: $\quad \mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } = 1.5 * 50$ (Total liters of mix) $\quad\quad\quad\quad\quad\mathrm { X } _ { 1 } \geq 0.48 * 1.5 * 50 \left( \mathrm { X } _ { 1 } \right.$ minimum) $\quad\quad\quad\quad\quad\mathrm { X } _ { 2 } \geq 0.5 ^ { * } 50 \left( \mathrm { X } _ { 2 } \right.$ minimum) $\quad\quad\quad\quad.0 .95 \mathrm { X } _ { 1 } + 0.78 \mathrm { X } _ { 2 } \geq 0.85 * 1.5 * 50$ (85\% alcohol minimum) $\quad\quad\quad\quad\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } \geq 0$ $Exhibit 3.3 The following questions are based on this problem and accompanying Excel windows. Jack's distillery blends scotches for local bars and saloons. One of his customers has requested a special blend of scotch targeted as a bar scotch. The customer wants the blend to involve two scotch products, call them A and B. Product A is a higher quality scotch while product B is a cheaper brand. The customer wants to make the claim the blend is closer to high quality than the alternative. The customer wants 50 1500 ml bottles of the blend. Each bottle must contain at least 48% of Product A and at least 500 ml of B. The customer also specified that the blend have an alcohol content of at least 85%. Product A contains 95% alcohol while product B contains 78%. The blend is sold for $12.50 per bottle. Product A costs $7 per liter and product B costs $3 per liter. The company wants to determine the blend that will meet the customer's requirements and maximize profit. Let \quad X _ { 1 } = Number of liters of product A _ { 1 } in total blend delivered \quad\quad\quad\mathrm { X } _ { 2 } = Number of liters of product \mathrm { B } in total blend delivered MIN: \quad 7 \mathrm { X } _ { 1 } + 3 \mathrm { X } _ { 2 } Subject to: \quad \mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } = 1.5 * 50 (Total liters of mix) \quad\quad\quad\quad\quad\mathrm { X } _ { 1 } \geq 0.48 * 1.5 * 50 \left( \mathrm { X } _ { 1 } \right. minimum) \quad\quad\quad\quad\quad\mathrm { X } _ { 2 } \geq 0.5 ^ { * } 50 \left( \mathrm { X } _ { 2 } \right. minimum) \quad\quad\quad\quad.0 .95 \mathrm { X } _ { 1 } + 0.78 \mathrm { X } _ { 2 } \geq 0.85 * 1.5 * 50 (85\% alcohol minimum) \quad\quad\quad\quad\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } \geq 0 -Refer to Exhibit 3.3. Which cells should be the constraint cells in this problem?$ -Refer to Exhibit 3.3. Which cells should be the constraint cells in this problem?

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Question 50

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. The following table summarizes the data for the problem. $\begin{array} { l | c c c c c } & \text { Profit per } & \text { Yield per } & \text { Maximum } & \text { Irrigation } &\text { Fertilizer }\\\text { Crop } &\text { Acre(\$)}&\text { Acre (lb) } & \text { Demand (lb) } & \text { (acre ft) }&\text { (pounds/acre) }\\ \hline \text { Corn } & 2,100 & 21,000 & 20,000 & 2 & 500 \\\text { pumpkin } & 900 & 10,000 & 180,000 & 3 & 400 \\\text { Beans } & 1,050 & 3,500 & \text { Ba,000 } & 1 & 300\end{array}$ What are the key formulas for this Excel spreadsheet implementation of the following formulation? Let = aces of carm = acres of punglan = acres of beans MAX: \ 2100+900+1050 Subject to: 21\leq200 10\leq180 3.5\leq80 2+3+1\leq50 5+4+3\leq80 ,\geq0 1 Farm Plenning Prablem 2 3 Carn Pumpkin Benns 4 Acres ta plant Tatal Prafit: 5 Prafit per acre 2100 900 1050 6 7 Constraints: Used Available 8 Corn denand 21000 200000 9 Pumpkin demand 10000 180000 10 Bean demand 3500 80000 11 Water 2 3 1 50 12 Fetilizer 500 400 300 8000

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Question 51

The "Objective Sense" option in the Risk Solver Platform (RSP) task pane may be used to

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Question 52

Robert Hope received a welcome surprise in this management science class; the instructor has decided to let each person define the percentage contribution to their grade for each of the graded instruments used in the class. These instruments were: homework, an individual project, a mid-term exam, and a final exam. Robert's grades on these instruments were 75, 94, 85, and 92, respectively. However, the instructor complicated Robert's task somewhat by adding the following stipulations: -homewark can account far up to $25 \%$ of the grade, but must be at least $5 \%$ af the grade; -the praject can account for up to $25 \%$ of the grade, but must be at least $5 \%$ af the grade; -the mid-term and final must each accaunt far betwen $10 \%$ and $40 \%$ of the grade but cannot accaunt far mare than $7 \%$ of the grade when the percentages are cambined; and -the project and final exam grades may not collectively constitute more than $50 \%$ of the Iratade. Formulate an LP model for Robert to maximize his numerical grade.

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Question 53

In the Risk Solver Platform (RSP) dialog box simple upper and lower bounds for decision variables are specified by

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Question 54

Exhibit 3.5 The following questions are based on this problem and accompanying Excel windows. A company is planning production for the next 4 quarters. They want to minimize the cost of production. The production cost is stable but demand and production capacity vary from quarter to quarter. The maximum amount of inventory which can be held is 12,000 units and management wants to keep at least 3,000 units on hand. Quarterly inventory holding cost is 3% of the cost of production. The company estimates the number of units carried in inventory each month by averaging the beginning and ending inventory for each month. There are currently 5,000 units in inventory. The company wants to produce at no less than one half of its maximum capacity in any quarter. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\text { Quarter }$ 1 2 3 4 Unit Production Cost \ 300 \ 300 \ 300 \ 300 Units Demanded 2,000 9,000 12,000 11,000 Maximum Production 8,000 7,000 8,000 9,000 Let = number of units produced in quarter i,i=1,\ldots,4 = beginning inventory for quarter i MiN: 300+300+300+300+ 9 + /2+9 + /2+9 + /2+9 + /2 Subject to: 4000\leq\leq8000 3500\leq\leq7000 4000\leq\leq8000 4500\leq\leq9000 3000\leq+-2000\leq12000 3000\leq+-9000\leq12000 3000\leq+-12000\leq12000 3000\leq+-11000\leq12000 =+-2000 =+-9000 =+-12000 =+-11000 ,\geq0 A 1 Quarter 2 1 2 3 4 3 Beginning Inventory 5,000 11,000 9,000 5,000 4 Units Produced 8,000 7,000 8,000 9,000 5 Units Demanded 2,000 9,000 12,000 11,000 6 Ending Inventory 11,000 9,000 5,000 3,000 7 8 Minimum Procduction 4,000 3,500 4,000 4,500 9 Maximum Froduction 8,000 7,000 8,000 9,000 10 11 Minimum Inventory 3,000 3,000 3,000 3,000 12 Maximum Inventory 12,000 12,000 12,000 12,000 13 14 Unit Production Cost \ 300 \ 300 \ 300 \ 300 15 Unit Carrying Cost 3.0\% \ 9,00 \ 9.00 \ 9,00 \ 9.00 16 17 Quarterly Production Cost \ 2,400,000 \ 2,100,000 \ 2,400,000 \ 2,700,000 18 Quarterly Carrying Cost \ 72,000 \ 90,000 \ 63,000 \ 36,000 19 20 Tota1 Cost \ 9,861,000 -Refer to Exhibit 3.5. Which cells are changing cells in the accompanying Excel spreadsheet?

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Question 55

What is the significance of an absolute cell reference in Excel?

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Question 56

A company needs to purchase several new machines to meet its future production needs. It can purchase three different types of machines A, B, and C. Each machine A costs $80,000 and requires 2,000 square feet of floor space. Each machine B costs $50,000 and requires 3,000 square feet of floor space. Each machine C costs $40,000 and requires 5,000 square feet of floor space. The machines can produce 200, 250 and 350 units per day respectively. The plant can only afford $500,000 for all the machines and has at most 20,000 square feet of room for the machines. The company wants to buy as many machines as possible to maximize daily production. Enter the numbers in the appropriate cells of range B5:F10 in the Excel spreadsheet to solve this problem based on the following formulation. Let $\quad \mathbf { x } _ { \mathrm { i } } =$ mumber of machines of type i purchased 200+250+300 2++\leq20 +50+40\leq500 ,\geq0 $A company needs to purchase several new machines to meet its future production needs. It can purchase three different types of machines A, B, and C. Each machine A costs $80,000 and requires 2,000 square feet of floor space. Each machine B costs $50,000 and requires 3,000 square feet of floor space. Each machine C costs $40,000 and requires 5,000 square feet of floor space. The machines can produce 200, 250 and 350 units per day respectively. The plant can only afford $500,000 for all the machines and has at most 20,000 square feet of room for the machines. The company wants to buy as many machines as possible to maximize daily production. Enter the numbers in the appropriate cells of range B5:F10 in the Excel spreadsheet to solve this problem based on the following formulation. Let \quad \mathbf { x } _ { \mathrm { i } } = mumber of machines of type i purchased \begin{array} { l } 200 X _ { 1 } + 250 X _ { 2 } + 300 X _ { 3 } \\ 2 \mathrm { X } _ { 1 } + \mathbf { 3 X _ { 2 } } + \mathbf { 5 X _ { 3 } } \leq 20 \\ \operatorname { gaX } _ { 1 } + 50 X _ { 2 } + 40 X _ { 3 } \leq 500 \\ X _ { 1 } , X _ { 7 } X _ { 3 } \geq 0 \\ \end{array}$

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Question 57

A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. There are only 50 acre ft of irrigation available and only 8,000 pounds/acre of fertilizer available. The following table summarizes the data for the problem. Crop Profit per Acre (\ ) Yield per Acre (Ib) Maximum Demand (Ib) Irrigation (acre ft) Fertilizer (pounds/acre) Corn 2,100 21,000 200,000 2 500 Pumpkin 900 10,000 180,000 3 400 Beans 1,050 3,500 80,000 1 300 Formulate the LP for this problem.

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Question 58

The constraints X₁ $\ge$ 0 and X₂ $\ge$ 0 are referred to as

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Question 59

You have been given the following linear programming model and Excel spreadsheet to solve this problem. What numbers should be entered into cells B5:C5 and B8:C10 to implement this model? MAX: 2+7 Subject to: 5+9\leq90 9+8\leq144 \leq8 ,\geq0 A B C D E 1 2 3 4 Number to make: OBJ. FN. VALUE 5 Unit profit: 6 7 Constraints: Used Available 8 1 90 9 2 144 10 3 8

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Question 60

Showing 41 - 60 of 88

Which type of spreadsheet cell represents the objective function in an LP model?

The "Objective Sense" option in the Risk Solver Platform (RSP) task pane may be used to

In the Risk Solver Platform (RSP) dialog box simple upper and lower bounds for decision variables are specified by

What is the significance of an absolute cell reference in Excel?

The constraints X₁ $\ge$ 0 and X₂ $\ge$ 0 are referred to as

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Sensitivity Analysis and the Simplex Method

Network Modeling

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

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Exam 3: Modeling and Solving Lp Problems in a Spreadsheet

Which type of spreadsheet cell represents the objective function in an LP model?

The "Objective Sense" option in the Risk Solver Platform (RSP) task pane may be used to

In the Risk Solver Platform (RSP) dialog box simple upper and lower bounds for decision variables are specified by

What is the significance of an absolute cell reference in Excel?

The constraints X1 ≥\ge≥ 0 and X2 ≥\ge≥ 0 are referred to as

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Sensitivity Analysis and the Simplex Method

Network Modeling

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Nonlinear Programming and Evolutionary Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

The constraints X₁ $\ge$ 0 and X₂ $\ge$ 0 are referred to as