Question 1

How many local minimum solutions are there on this graph of a function Mark their locations on the graph.

Accepted Answer

There are three loca

Question 2

In a maximization problem, the GRG algorithm's search for a feasible direction of improvement equates to ____ in the simplex algorithm for LP problems.

Accepted Answer

A)  an adjacent corner point 
B)  a zero reduced cost 
C)  a positive shadow price 
D)  a positive reduced cost 
A)  an adjacent corner point 
B)  a zero reduced cost 
C)  a positive shadow price 
D)  a positive reduced cost

Question 3

Exhibit 8.1
The following questions pertain to the problem and spreadsheet below.
A company makes products A and B from 2 resources, labor and material. The company wants to determine the selling price which will maximize profits. A unit of A costs 25 to make and demand is estimated to be 20 - .10 * Price of A. A unit of B costs 18 to make and demand is estimated to be 30 - .07 * Price of B. The utilization of labor and materials and the available quantity of resources is shown in the table. A reasonable price for the products is between 100 and 200.
 $\begin{array}{lllc}
\text { Product } & \text { A } & \text { B } & \text { Available resources } \
\hline \text { Labor (hr/unit) } & 3 & 2 & 150 \
\text { Material (ounces/unit) } & 1 & 2 & 200 \
\text { Manufacturing cost }(\$ / \text { unit) } & 25 & 18 & \
\text { Demand (units) } & 20-0.10^{*} P_{1}& 30-0.07^{*} P_{2} &
\end{array}$
 Let XS1U1B11S1U1B0 = demand for As and XS1U1B12S1U1B0 = demand for Bs.
Let PS1U1B11S1U1B0 = price for As and PS1U1B12S1U1B0 = price for Bs
 $\begin{array}{|c|l|c|c|c|c|}  
\hline& \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\hline 1 & & & & & \
\hline 2 & & \mathrm{~A} & \mathrm{~B} & & \
\hline 3 & \text { Price } & 112.50 & 223.29 & & \
\hline 4 & \text { Marginal Cost } & 25.00 & 18.00 & & \
\hline 5 & \text { Profit Margin } & 87.50 & 205.29 & & \
\hline 6 & & & & & \
\hline 7 & \text { Demand } & 8.75 & 14.37 & & \
\hline 8 & & & & & \
\hline 9 & \text { Total Profit } & 3715.58 & & & \
\hline 10 & & & & & \
\hline 11 & \text { Constraints: } & &&\text { Used } & \text { Available }\
\hline 12 & \text { Labor } & 3.00 & 2.00 & 54.99 & 150.00 \
\hline 13 & \text { Material } & 1.00 & 2.00 & 37.49 & 200.00 \
\hline
\end{array}$

-Refer to Exhibit 8.1. What formula is used in cell B7 of the spreadsheet for this problem?

Accepted Answer

A)  = 30-.07 * C3 
B)  = 20 - .1 * B3 
C)  = B3- B4 
D)  = B5 * B7 + C5 * C7 
A)  = 30-.07 * C3 
B)  = 20 - .1 * B3 
C)  = B3- B4 
D)  = B5 * B7 + C5 * C7

Question 4

A company makes products A and B from 2 resources, labor and material. The company wants to determine the selling price which will maximize profits. A unit of A costs 30 to make and demand is estimated to be 50- 0.09 * Price of A. A unit of B costs 20 to make and demand is estimated to be 30- 0.14 * Price of B. The utilization of labor and materials and the available quantity of resources is shown in the table. A reasonable price for the products is between 90 and 140.
 $\begin{array}{lllc}
\text { Product } & \text { A } & \text { B } & \text { Available resources } \
\hline \text { Labor (hr/unit) } & 2 & 4 & 150 \
\text { Material (ounces/unit) } & 2 & 8 & 220 \
\text { Manufacturing cost(\$/unit) } & 30 & 20 & \
\text { Demand (units) } & 50-0.09 * P_{1} & 30-0.14 * P_{2} &
\end{array}$

Let X1 = demand for As and X2 = demand for Bs.
Let P1 = price for As and P2 = price for Bs.
The NLP for the problem is:
 $\text {MAX}$: $52.70 P _ { 1 } - 0.09 P _ { 1 } ^ { 2 } + 32.80 P _ { 2 } - 0.14 P _ { 2 } ^ { 2 } - 2100$
$\text {Subject to:}$
$\begin{array}{l}
\mathrm{X}_{1}-50+0.09 \mathrm{P}_{1}=0 \
\mathrm{X}_{2}-30+0.14 \mathrm{P}_{2}=0 \
2 \mathrm{X}_{1}+4 \mathrm{X}_{2} \leq 150 \
2 \mathrm{X}_{1}+8 \mathrm{X}_{2} \leq 220 \
90 \leq \mathrm{P}_{1}, \mathrm{P}_{2} \leq 140 \
\mathrm{X}_{1}, \mathrm{X}_{2} \geq 0 \
\text { and the solution }\left(\mathrm{P}_{1}, \mathrm{P}_{2}\right)=(140.0,117.14)
\end{array}$  What values should go in cells B3:E18 of the spreadsheet for this problem?
 $\begin{array}{|c|l|c|c|c|c|}
\hline &{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } \
\hline 1 & & & & & \
\hline 2 & & \text { A } & \text { B } & & \
\hline 3 & \text { Price } & & & & \
\hline 4 & \text { Min Price } & & & & \
\hline 5 & \text { Max Price } & & & & \
\hline 6 & \text { Marginal Cost } & & & & \
\hline 7 & \text { Profit Margin } & & & & \
\hline 8 & & & & & \
\hline 9 & \text { Demand } & & & & \
\hline 10 & & & & & \
\hline 11 & \text { Total Profit } & & & & \
\hline 12 & & & & & \
\hline 13 & \text { Constraints: } & & & \text { Used } & \text { Available } \
\hline 14 & \text { Labor } & & & & \
\hline 15 & \text { Material } & & & & \
\hline 
\end{array}$.

Accepted Answer

None

Question 5

How many local maximum solutions are there on this graph of a function? Mark their locations on the graph.

Accepted Answer

There two local maxi

Question 6

If the "Standard LP/Quadratic Engine" option is chosen in the Risk Solver Platform (RSP) task pane, RSP

Accepted Answer

A)  will test for non-linearity in the model and apply GRG. 
B)  will test for non-linearity in the model and apply Simplex. 
C)  uses the B & B algorithm to solve the problem. 
D)  will apply Simplex if the linearity test passes. 
A)  will test for non-linearity in the model and apply GRG. 
B)  will test for non-linearity in the model and apply Simplex. 
C)  uses the B & B algorithm to solve the problem. 
D)  will apply Simplex if the linearity test passes.

Question 7

An office supply company is attempting to determine the order quantity for Mt. White fountain pens which are sold to local executives. Annual demand is 5,000 units and each pen costs the store $50. It costs $75 to place an order and the inventory carrying cost rate is 30% of the value of the item.
Formulate the objective function for this problem. Let Q indicate the order quantity.

Accepted Answer

MIN: 5000

Question 8

Find the maximum solution on this graph of a function starting from X = 12. Mark its location on the graph.

Accepted Answer

The maximu

Question 9

An investor wants to determine how much interest he must earn to be able to make the payments on a 10-year mortgage which has increasing annual payments. The problem is summarized in the accompanying spreadsheet. The investor has enough money to make an initial investment of $12,000 and hopes he can earn 18% on his investments. He would like to know how low his annual return can be and still allow him to make his payments from interest income.
What formulas should go in cells B7:F7 of the spreadsheet for this problem?

Accepted Answer

The answer of An investor wants to determine how much...

Question 10

A company makes products A and B from 2 resources, labor and material. The company wants to determine the selling price which will maximize profits. A unit of product A costs 25 to make and demand is estimated to be 20 F1F1F1S1?F1F1F10 .10 * Price of A. A unit of product B costs 18 to make and demand is estimated to be 30 F1F1F1S1?F1F1F10 .07 * Price of B. The utilization of labor and materials and the available quantity of resources is shown in the table. A reasonable price for the products is between 100 and 200. $\begin{array}{lllc}
\text { Product } & \text { A } & \text { B } & \text { Available resources } \
\hline \text { Labor (hr/unit) } & 3 & 2 & 150 \
\text { Material (ounces/unit) } & 1 & 2 & 200 \
\text { Manufacturing cost }(\$ / \text { unit) } & 25 & 18 & \
\text { Demand (units) } & 20-0.10^{*} P_{1}& 30-0.07^{*} P_{2} &
\end{array}$
 Let X1 = demand for As and X2 = demand for Bs.
Let P1 = price for As and P2 = price for Bs.
The objective function for this problem is?

Accepted Answer

A)  MAX 25 X1 + 18 X2 
B)  MAX (20 F1F1F1S1?F1F1F10 0.10*P1) X1 + (30 F1F1F1S1?F1F1F10 0.07*P2) X2 
C)  MAX 20 P1 F1F1F1S1?F1F1F10 0.1 P12 + 30 P2 F1F1F1S1?F1F1F10 0.07 P22 F1F1F1S1?F1F1F10 1040 
D)  MAX 22.5 P1 F1F1F1S1?F1F1F10 0.1 P12 + 31.26 P2 F1F1F1S1?F1F1F10 0.07 P22 F1F1F1S1?F1F1F10 1040 
A)  MAX 25 X1 + 18 X2 
B)  MAX (20 F1F1F1S1?F1F1F10 0.10*P1) X1 + (30 F1F1F1S1?F1F1F10 0.07*P2) X2 
C)  MAX 20 P1 F1F1F1S1?F1F1F10 0.1 P12 + 30 P2 F1F1F1S1?F1F1F10 0.07 P22 F1F1F1S1?F1F1F10 1040 
D)  MAX 22.5 P1 F1F1F1S1?F1F1F10 0.1 P12 + 31.26 P2 F1F1F1S1?F1F1F10 0.07 P22 F1F1F1S1?F1F1F10 1040

Question 11

An investor is developing a portfolio of stocks. She has identified 3 stocks to invest in. She wants to earn at least 5% return but with minimum risk. The problem data is given in the following Excel spreadsheet. What formula should be entered in cell G4 of the Excel spreadsheet?

Accepted Answer

A)  =COVAR(B4:B13) 
B)  =VARP(B4:B13) 
C)  =COVAR(B4:D13,$D$4:$B$13) 
D)  =COVAR(B4:B13,$B$4:$B$13) 
A)  =COVAR(B4:B13) 
B)  =VARP(B4:B13) 
C)  =COVAR(B4:D13,$D$4:$B$13) 
D)  =COVAR(B4:B13,$B$4:$B$13)

Question 12

An investor is developing a portfolio of stocks. She has identified 3 stocks in which to invest. She wants to earn at least 11% return but with minimum risk.
The average return for the stocks is:
 $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\underline{\text { Annual Return }}$
$\begin{array}{lccc} 
& \text { A } & \text { B } & \text { C } \
\text { Average } & 10.72 \% & 10.68 \% & 11.87 \%
\end{array}$
 The covariance matrix for the stocks is:
 $$\begin{array} { c r r r } 
& \text { A } & \text { B } & \text { C } \
\hline \text { A } & 0.00009 & - 0.00009 & - 0.00011 \
\text { B } & - 0.00009 & 0.00032 & - 0.00007 \
\text { C } & - 0.00011 & - 0.00007 & 0.00122
\end{array}$$ Let: Pi  = proportion of total funds invested in i, i = A, B, C
Formulate the NLP for this problem.

Accepted Answer

Question 13

In NLP a local optimum is best described as

Accepted Answer

A)  an interior point. 
B)  a corner point. 
C)  a point yielding no improving direction. 
D)  a good starting point for subsequent searches. 
A)  an interior point. 
B)  a corner point. 
C)  a point yielding no improving direction. 
D)  a good starting point for subsequent searches.

Question 14

Exhibit 8.1
The following questions pertain to the problem and spreadsheet below.
A company makes products A and B from 2 resources, labor and material. The company wants to determine the selling price which will maximize profits. A unit of A costs 25 to make and demand is estimated to be 20 - .10 * Price of A. A unit of B costs 18 to make and demand is estimated to be 30 - .07 * Price of B. The utilization of labor and materials and the available quantity of resources is shown in the table. A reasonable price for the products is between 100 and 200.
 $\begin{array}{lllc}
\text { Product } & \text { A } & \text { B } & \text { Available resources } \
\hline \text { Labor (hr/unit) } & 3 & 2 & 150 \
\text { Material (ounces/unit) } & 1 & 2 & 200 \
\text { Manufacturing cost }(\$ / \text { unit) } & 25 & 18 & \
\text { Demand (units) } & 20-0.10^{*} P_{1}& 30-0.07^{*} P_{2} &
\end{array}$
 Let XS1U1B11S1U1B0 = demand for As and XS1U1B12S1U1B0 = demand for Bs.
Let PS1U1B11S1U1B0 = price for As and PS1U1B12S1U1B0 = price for Bs
 $\begin{array}{|c|l|c|c|c|c|}  
\hline& \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\hline 1 & & & & & \
\hline 2 & & \mathrm{~A} & \mathrm{~B} & & \
\hline 3 & \text { Price } & 112.50 & 223.29 & & \
\hline 4 & \text { Marginal Cost } & 25.00 & 18.00 & & \
\hline 5 & \text { Profit Margin } & 87.50 & 205.29 & & \
\hline 6 & & & & & \
\hline 7 & \text { Demand } & 8.75 & 14.37 & & \
\hline 8 & & & & & \
\hline 9 & \text { Total Profit } & 3715.58 & & & \
\hline 10 & & & & & \
\hline 11 & \text { Constraints: } & &&\text { Used } & \text { Available }\
\hline 12 & \text { Labor } & 3.00 & 2.00 & 54.99 & 150.00 \
\hline 13 & \text { Material } & 1.00 & 2.00 & 37.49 & 200.00 \
\hline
\end{array}$

-Refer to Exhibit 8.1. What formula is used in cell B9 of the spreadsheet for this problem?

Accepted Answer

A)  =B3*B7+C3*C7 
B)  =B5*B7+C5*C7 
C)  =(B5-B4)*B7+(C5-C4)*B7 
D)  =B3*B7+C3*B7+B4*B7+C4*B7 
A)  =B3*B7+C3*C7 
B)  =B5*B7+C5*C7 
C)  =(B5-B4)*B7+(C5-C4)*B7 
D)  =B3*B7+C3*B7+B4*B7+C4*B7

Question 15

How much must the objective function coefficient of the variable Pumpkin change before any Pumpkins are produced based on the following sensitivity report? $\text { Changing Cells }$
$\begin{array}{llrr}
&&\text { Final}& \text { Reduced }\ 
\text { Cell } & \text { Name } & \text { Value } & \text { Gradient } \
\hline \$ \mathrm{~B} \$ 4 & \text { Corn } & 9.52 & 0 \
\$ \mathrm{C} \$ 4 & \text { Pumplsin } & 0 & -499.99 \
\$ \mathrm{D} \$ 4 & \text { Beans } & 10.79 & 0
\end{array}$

$\text { Constraints }$ 
$\begin{array}{llrr}
&&\text { Final}& \text { Reduced }\  
\text { Cell } & \text { Name } & \text { Value } & \text { Multiplier } \
\hline \$ E \$ 8 & \text { Corn } & 200000 & 0.016 \
\$ E \$ 9 & \text { Pumplkin } & 99 & 12 \
\$ E \$ 10 & \text { Beans } & 37777.78 & 0 \
\$ E \$ 11 & \text { Water } & 29.84 & 0 \
\$ E \$ 12 & \text { Fertilizer } & 8000 & 3.49
\end{array}$

Accepted Answer

A)  increase by 12 
B)  decrease by 12 
C)  increase by 499.99 
D)  decrease by 499.99 
A)  increase by 12 
B)  decrease by 12 
C)  increase by 499.99 
D)  decrease by 499.99

Question 16

The GRG and Simplex algorithms are similar in that

Accepted Answer

A)  each algorithm process continues until there is no further improvement in the objective function. 
B)  both algorithms take their starting solution from the spreadsheet. 
C)  both return the globally optimal solution. 
D)  both algorithms return a solution that satisfies at least one constraint at equality. 
A)  each algorithm process continues until there is no further improvement in the objective function. 
B)  both algorithms take their starting solution from the spreadsheet. 
C)  both return the globally optimal solution. 
D)  both algorithms return a solution that satisfies at least one constraint at equality.

Question 17

Which of the following is not an assumption of an EOQ problem.

Accepted Answer

A)  Demand for a product is fairly constant. 
B)  Inventory depletion rates vary non-linearly. 
C)  Each new order is delivered in full when the inventory level reaches 0. 
D)  All are valid assumptions. 
A)  Demand for a product is fairly constant. 
B)  Inventory depletion rates vary non-linearly. 
C)  Each new order is delivered in full when the inventory level reaches 0. 
D)  All are valid assumptions.

Question 18

Exhibit 8.2
The following questions pertain to the problem and spreadsheet below.
A construction company just purchased a 300 x 300 foot lot upon which they plan to build an office building. They need at least 60,000 ftS1U1P12S1S1P0 of office floor space. Zoning regulations require each floor be 10 feet high and the building not exceed 65 ft in height. Further, parking space must equal at least 30% of the total floor space available. The company's cost accountant uses a 60% factor of the building height and a 1% factor of any story's floor area to calculate the total building cost (in millions of dollars).
The following is the NLP formulation for the problem.
   The spreadsheet implementation of this formulation applies to the following questions.
 $\begin{array}{|c|l|c|c|c|c|} 
\hline &{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } \
\hline 1 & & \text { Length } & \text { Width } & \text { Stories } & \text { Parking } \  
\hline 2 & & 108.39492 & 92.255243 & 6 & 80,000 \
\hline 3 & \text { Max Values } & 300 & 300 & 6 & \
\hline 4 & & & & & \
\hline 5 & \text { Total Floor Area } & 60,000 & \geq & 60,000 & \
\hline 6 & \text { Total Lot Area } & 90,000 & = & 90,000 & \
\hline 7 & \text { Min. Parking Area } & 65,000 & \geq & 0 & \
\hline 8 & \text { Max. Bld Height } & 60 & \leq & 65 & \
\hline 9 & & & & & \
\hline 10 & \text { Cost } & & & & \
\hline 11 & \text { Height Factor } & 0.6 & \text { Total Height } & 60 & \
\hline 12 & \text { Area Factor } & 0.01 & \text { Floor Area } & 10,000 & \
\hline 13 & & & \text { Cost } & \$ 136.0 & \text { millions } \$ \
\hline
\end{array}$

-Refer to Exhibit 8.2. What formula would you place into cell B5 to calculate Total Floor Area?

Accepted Answer

The answer of Exhibit 8.2
The following questions pertain to the...

Question 19

An office supply company is attempting to determine the order quantity for laser printer toner cartridges which are sold to local businesses. Annual demand is 20,000 units and each cartridge costs the store $25. It costs $30 to place an order and the inventory carrying cost rate is 25% of the value of the item. The following spreadsheet has been set up to solve the problem. What cell is the variable cell in this problem? $\begin{array}{|c|c|c|} 
\hline& \text { A } & \text { B } \ 
\hline 1 & & \
\hline 2 & & \
\hline 3 & \text { Annual Demand: } & 20,000 \
\hline 4 & & \
\hline 5 & \text { Cost per Unit: } & \$ 25 \
\hline 6 & \text { Ordering Cost: } & \$ 30 \
\hline 7 & \text { Carrying Cost: } & 25 \% \
\hline 8 & & \
\hline 9 & \text { Order Quantity: } & 483.73 \
\hline 10 & & \
\hline 11 & \text { Total Cost: } & \$ 502,738.61 \
\hline
\end{array}$

Accepted Answer

A)  B3 
B)  B7 
C)  B9 
D)  B11 
A)  B3 
B)  B7 
C)  B9 
D)  B11

Question 20

An office supply company is attempting to determine the order quantity for laser printer toner cartridges which are sold to local businesses. Annual demand is 20,000 units and each cartridge costs the store $25. It costs $30 to place an order and the inventory carrying cost rate is 25% of the value of the item. The following spreadsheet has been set up to solve the problem. What cell is the objective cell in this problem? $\begin{array}{|c|c|c|} 
\hline& \text { A } & \text { B } \
\hline 1 & & \
\hline 2 & & \
\hline 3 & \text { Annual Demand: } & 20,000 \
\hline 4 & & \
\hline 5 & \text { Cost per Unit: } & \$ 25 \
\hline 6 & \text { Ordering Cost: } & \$ 30 \
\hline 7 & \text { Carrying Cost: } & 25 \% \
\hline 8 & & \
\hline 9 & \text { Order Quantity: } & 483.73 \
\hline 10 & & \
\hline 11 & \text { Total Cost: } & \$ 502,738.61 \
\hline 
\end{array}$

Accepted Answer

A)  B3 
B)  B7 
C)  B9 
D)  B11 
A)  B3 
B)  B7 
C)  B9 
D)  B11

How many local minimum solutions are there on this graph of a function Mark their locations on the graph.

In a maximization problem, the GRG algorithm's search for a feasible direction of improvement equates to ____ in the simplex algorithm for LP problems.

How many local maximum solutions are there on this graph of a function? Mark their locations on the graph.

If the "Standard LP/Quadratic Engine" option is chosen in the Risk Solver Platform (RSP) task pane, RSP

Find the maximum solution on this graph of a function starting from X = 12. Mark its location on the graph.

An investor is developing a portfolio of stocks. She has identified 3 stocks to invest in. She wants to earn at least 5% return but with minimum risk. The problem data is given in the following Excel spreadsheet. What formula should be entered in cell G4 of the Excel spreadsheet?

In NLP a local optimum is best described as

The GRG and Simplex algorithms are similar in that

Which of the following is not an assumption of an EOQ problem.

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Sensitivity Analysis and the Simplex Method

Network Modeling

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

Exam 8: Nonlinear Programming and Evolutionary Optimization

How many local minimum solutions are there on this graph of a function Mark their locations on the graph.

In a maximization problem, the GRG algorithm's search for a feasible direction of improvement equates to ____ in the simplex algorithm for LP problems.

How many local maximum solutions are there on this graph of a function? Mark their locations on the graph.

If the "Standard LP/Quadratic Engine" option is chosen in the Risk Solver Platform (RSP) task pane, RSP

Find the maximum solution on this graph of a function starting from X = 12. Mark its location on the graph.

An investor is developing a portfolio of stocks. She has identified 3 stocks to invest in. She wants to earn at least 5% return but with minimum risk. The problem data is given in the following Excel spreadsheet. What formula should be entered in cell G4 of the Excel spreadsheet?

In NLP a local optimum is best described as

The GRG and Simplex algorithms are similar in that

Which of the following is not an assumption of an EOQ problem.

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Sensitivity Analysis and the Simplex Method

Network Modeling

Integer Linear Programming

Goal Programming and Multiple Objective Optimization

Regression Analysis

Discriminant Analysis

Time Series Forecasting

Introduction to Simulation Using Risk Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters