Question 1

The feasible region in the diagram below is consistent with which one of the following constraints?

Accepted Answer

A)  8X1 + 4X2 ≤ 160 
B)  8X1 + 4X2 ≥ 160 
C)  4X1 + 8X2 ≤ 160 
D)  8X1 - 4X2 ≤ 160 
E)  4X1 - 8X2 ≤ 160 
A)  8X1 + 4X2 ≤ 160 
B)  8X1 + 4X2 ≥ 160 
C)  4X1 + 8X2 ≤ 160 
D)  8X1 - 4X2 ≤ 160 
E)  4X1 - 8X2 ≤ 160

Question 2

A common form of the product-mix linear programming problem seeks to find that combination of products and the quantity of each that maximizes profit in the presence of limited resources.

Accepted Answer

A) True 
 B)False

Question 3

Consider the following constraints from a two-variable linear program. (1) X ≥1
(2) Y ≥1
(3) X + Y ≤ 9
If these are the only constraints, which of the following points (X, Y) cannot be the optimal solution?

Accepted Answer

A)  (1, 1) 
B)  (1, 8) 
C)  (8, 1) 
D)  (4, 4) 
E)  The question cannot be answered without knowing the objective function. 
A)  (1, 1) 
B)  (1, 8) 
C)  (8, 1) 
D)  (4, 4) 
E)  The question cannot be answered without knowing the objective function.

Question 4

The requirements of linear programming problems include an objective function, the presence of constraints, objective and constraints expressed in linear equalities or inequalities, and __________.

Accepted Answer

alternativ

Question 5

Two methods of solving linear programming problems by hand include the corner-point method and the__________.

Accepted Answer

iso-profit

Question 6

The feasible region in the diagram below is consistent with which one of the following constraints?

Accepted Answer

A)  8X1 + 4X2 ≥ 160 
B)  4X1 + 8X2 ≤ 160 
C)  8X1 - 4X2 ≤ 160 
D)  8X1 + 4X2 ≤ 160 
E)  4X1 - 8X2 ≤ 160 
A)  8X1 + 4X2 ≥ 160 
B)  4X1 + 8X2 ≤ 160 
C)  8X1 - 4X2 ≤ 160 
D)  8X1 + 4X2 ≤ 160 
E)  4X1 - 8X2 ≤ 160

Question 7

If cars sell for $500 profit and trucks sell for $300 profit which of the following represents the objective function?

Accepted Answer

A)  Maximize = 500C+300T 
B)  Minimize = 500C + 300T 
C)  Maximize = 500C - 300T 
D)  Minimize = 300T- 500C 
E)  None of the above 
A)  Maximize = 500C+300T 
B)  Minimize = 500C + 300T 
C)  Maximize = 500C - 300T 
D)  Minimize = 300T- 500C 
E)  None of the above

Question 8

South Coast Papers wants to mix two lubricating oils (A and B) for its machines in order to minimize cost. It needs no less than 3,000 gallons in order to run its machines during the next month. It has a maximum oil storage capacity of 4,000 gallons. There are 2,000 gallons of Oil A and 4,000 of Oil B available. The mixed fuel must have a viscosity rating of no less than 40.
When mixing fuels, the amount of oil obtained is exactly equal to the sum of the amounts put in. The viscosity rating is the weighted average of the individual viscosities, weighted in proportion to their volumes. The following is known: Oil A has a viscosity of 45 and costs 60 cents per gallon; Oil B has a viscosity of 37.5 and costs 40 cents per gallon.
State the objective and the constraints of this problem. Plot all constraints and highlight the feasible region. Use your (by now, well-developed) intuition to suggest a feasible (but not necessarily optimal) solution. Be certain to show that your solution meets all constraints.

Accepted Answer

The problem formulation appears below. T

Question 9

Using the iso-profit line solution method to solve a maximization problem requires that we

Accepted Answer

A)  find the value of the objective function at the origin 
B)  move the iso-profit line away from the origin until it barely touches some part of the feasible region 
C)  move the iso-cost line to the lowest level that still touches some part of the feasible region 
D)  test the objective function value of every corner point in the feasible region 
E)  none of the above 
A)  find the value of the objective function at the origin 
B)  move the iso-profit line away from the origin until it barely touches some part of the feasible region 
C)  move the iso-cost line to the lowest level that still touches some part of the feasible region 
D)  test the objective function value of every corner point in the feasible region 
E)  none of the above

Question 10

Suppose that an iso-profit line is given to be X+Y=15. What would be the profit made from producing 20X and 10Y?

Accepted Answer

A)  15 
B)  30 
C)  0 
D)  20X and 10Y is not a feasible solution. 
E)  Unable to determine 
A)  15 
B)  30 
C)  0 
D)  20X and 10Y is not a feasible solution. 
E)  Unable to determine

Question 11

An iso-profit line

Accepted Answer

A)  can be used to help solve a profit maximizing linear programming problem 
B)  is parallel to all other iso-profit lines in the same problem 
C)  is a line with the same profit at all points 
D)  all of the above 
E)  none of the above 
A)  can be used to help solve a profit maximizing linear programming problem 
B)  is parallel to all other iso-profit lines in the same problem 
C)  is a line with the same profit at all points 
D)  all of the above 
E)  none of the above

Question 12

What is sensitivity analysis?

Accepted Answer

Sensitivity analysis projects

Question 13

The optimal solution of a linear programming problem that consists of two variables and six constraints will probably not satisfy all six constraints as equalities.

Accepted Answer

A) True 
 B)False

Question 14

The property manager of a city government issues chairs, desks, and other office furniture to city buildings from a centralized distribution center. Like most government agencies, it operates to minimize its costs of operations. In this distribution center, there are two types of standard office chairs, Model A and Model B. Model A is considerably heavier than Model B, and costs $20 per chair to transport to any city building; each model B costs $14 to transport. The distribution center has on hand 400 chairs-200 each of A and B.
The requirements for shipments to each of the city's buildings are as follows:
Building 1 needs at least 100 of A
Building 2 needs at least 150 of B.
Building 3 needs at least 100 chairs, but they can be of either type, mixed.
Building 4 needs 40 chairs, but at least as many B as A.
Write out the objective function and the constraints for this problem. (Hint: there are eight variables-chairs for building 1 cannot be used to satisfy the demands for another building).

Accepted Answer

Let the variables be A1, A2, A3, and A4

Question 15

A maximizing linear programming problem with constraints C1, C2, and C3 has been solved. The dual values associated with the problem are C1 = $2, C2 = $0.50, and C3 = $0. Which statement below is False?

Accepted Answer

A)  One more unit of the resource in C1 would add $2 to the objective function value. 
B)  One more unit of the resource in C2 would add one more unit each of X and Y. 
C)  The resource in C3 has not been used up 
D)  The resources in C1 and in C2, but not in C3, are scarce. 
E)  All of the above are true. 
A)  One more unit of the resource in C1 would add $2 to the objective function value. 
B)  One more unit of the resource in C2 would add one more unit each of X and Y. 
C)  The resource in C3 has not been used up 
D)  The resources in C1 and in C2, but not in C3, are scarce. 
E)  All of the above are true.

Question 16

What combination of x and y will yield the optimum for this problem?
Minimize $3x + $15y, subject to (1) 2x + 4y < 12 and (2) 5x + 2y < 10 and (3) x, y ≥ 0.

Accepted Answer

A)  x = 2, y = 0 
B)  x = 0, y = 3 
C)  x = 0, y = 0 
D)  x = 1, y = 5 
E)  none of the above 
A)  x = 2, y = 0 
B)  x = 0, y = 3 
C)  x = 0, y = 0 
D)  x = 1, y = 5 
E)  none of the above

Question 17

Which of the following combinations of constraints has no feasible region?

Accepted Answer

A) X + Y > 15 and X - Y 5 and X > 10 C) X > 10 and Y > 20 D) X + Y > 100 and X + Y < 50 E) All of the above have a feasible region. A) X + Y > 15 and X - Y 5 and X > 10 C) X > 10 and Y > 20 D) X + Y > 100 and X + Y < 50 E) All of the above have a feasible region.

Question 18

For a linear programming problem with the constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, two of its corner points are (0, 0) and (0, 25).

Accepted Answer

A) True 
 B)False

Question 19

Which of the following sets of constraints results in an unbounded maximizing problem?

Accepted Answer

A) X + Y > 100 and X + Y 15 and X - Y 5 D) X < 10 and Y < 20 E) All of the above have a bounded maximum. A) X + Y > 100 and X + Y 15 and X - Y 5 D) X < 10 and Y < 20 E) All of the above have a bounded maximum.

Question 20

In which of the following has LP been applied successfully?

Accepted Answer

A)  minimizing distance traveled by school buses carrying children 
B)  minimizing 911 response time for police patrols 
C)  minimizing labor costs for bank tellers while maintaining service levels 
D)  determining the distribution system for multiple warehouses to multiple destinations 
E)  all of the above 
A)  minimizing distance traveled by school buses carrying children 
B)  minimizing 911 response time for police patrols 
C)  minimizing labor costs for bank tellers while maintaining service levels 
D)  determining the distribution system for multiple warehouses to multiple destinations 
E)  all of the above

Exam 22: Linear Programming

The feasible region in the diagram below is consistent with which one of the following constraints?

A common form of the product-mix linear programming problem seeks to find that combination of products and the quantity of each that maximizes profit in the presence of limited resources.

Consider the following constraints from a two-variable linear program. (1) X ≥1 (2) Y ≥1 (3) X + Y ≤ 9 If these are the only constraints, which of the following points (X, Y) cannot be the optimal solution?

The requirements of linear programming problems include an objective function, the presence of constraints, objective and constraints expressed in linear equalities or inequalities, and __________.

Two methods of solving linear programming problems by hand include the corner-point method and the__________.

The feasible region in the diagram below is consistent with which one of the following constraints?

If cars sell for $500 profit and trucks sell for $300 profit which of the following represents the objective function?

Using the iso-profit line solution method to solve a maximization problem requires that we

Suppose that an iso-profit line is given to be X+Y=15. What would be the profit made from producing 20X and 10Y?

An iso-profit line

What is sensitivity analysis?

The optimal solution of a linear programming problem that consists of two variables and six constraints will probably not satisfy all six constraints as equalities.

A maximizing linear programming problem with constraints C1, C2, and C3 has been solved. The dual values associated with the problem are C1 = $2, C2 = $0.50, and C3 = $0. Which statement below is False?

What combination of x and y will yield the optimum for this problem? Minimize $3x + $15y, subject to (1) 2x + 4y < 12 and (2) 5x + 2y < 10 and (3) x, y ≥ 0.

Which of the following combinations of constraints has no feasible region?

For a linear programming problem with the constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, two of its corner points are (0, 0) and (0, 25).

Which of the following sets of constraints results in an unbounded maximizing problem?

In which of the following has LP been applied successfully?

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