Question 1

A synonym for shadow price is ________.

Accepted Answer

The answer of A synonym for shadow price is ________....

Question 2

Suppose that an iso-profit line is given to be X + Y = 10.Which of the following represents another iso-profit line for the same scenario?

Accepted Answer

A) X + Y = 15 
B) X - Y = 10 
C) Y - X = 10 
D) 2X + Y = 10 
E) none of the above 
A) X + Y = 15 
B) X - Y = 10 
C) Y - X = 10 
D) 2X + Y = 10 
E) none of the above

Question 3

Describe how to incorporate fixed costs into a cost-minimizing linear program,where the fixed cost of using a machine is incurred if any products are produced on that machine.

Accepted Answer

Introduce a binary variable for each mac

Question 4

A linear programming problem contains a restriction that reads "the quantity of Q must be no larger than the sum of R,S,and T." Formulate this as a linear programming constraint.

Accepted Answer

A) Q + R + S + T ≤ 4 
B) Q ≥ R + S + T 
C) Q - R - S - T ≤ 0 
D) Q / (R + S + T)≤ 0 
E) Q ≤ R + Q ≤ S + Q ≤ T 
A) Q + R + S + T ≤ 4 
B) Q ≥ R + S + T 
C) Q - R - S - T ≤ 0 
D) Q / (R + S + T)≤ 0 
E) Q ≤ R + Q ≤ S + Q ≤ T

Question 5

What is the simplex method?

Accepted Answer

The simplex method i

Question 6

The ________ is a mathematical expression in linear programming that maximizes or minimizes some quantity.

Accepted Answer

The answer of The ________ is a mathematical expression in...

Question 7

A manager must decide on the mix of products to produce for the coming week.Product A requires three minutes per unit for molding,two minutes per unit for painting,and one minute for packing.Product B requires two minutes per unit for molding,four minutes for painting,and three minutes per unit for packing.There will be 600 minutes available for molding,600 minutes for painting,and 420 minutes for packing.Both products have contributions of $1.50 per unit.
a.Algebraically state the objective and constraints of this problem.
b.Plot the constraints on the grid below and identify the feasible region.

Accepted Answer

The objective of the problem i

Question 8

The optimal solution to a linear programming problem lies within the feasible region.

Accepted Answer

A) True 
 B)False

Question 9

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

Question 10

Linear programming is an appropriate problem-solving technique for decisions that have no alternative courses of action.

Accepted Answer

A) True 
 B)False

Question 11

For the constraints given below,which point is in the feasible region of this maximization problem? (1)14x + 6y ≤ 42 (2)x - y ≤ 3 (3)x,y ≥ 0

Accepted Answer

A) x = 2,y = 1 
B) x = 1,y = 5 
C) x = -1,y = 1 
D) x = 4,y = 4 
E) x = 2,y = 8 
A) x = 2,y = 1 
B) x = 1,y = 5 
C) x = -1,y = 1 
D) x = 4,y = 4 
E) x = 2,y = 8

Question 12

Which of the following represents a valid constraint in linear programming?

Accepted Answer

A) 2X ≥ 7XY 
B) (2X)(7Y)≥ 500 
C) 2X + 7Y ≥100 
D) 2X2 + 7Y ≥ 50 
E) All of the above are valid linear programming constraints. 
A) 2X ≥ 7XY 
B) (2X)(7Y)≥ 500 
C) 2X + 7Y ≥100 
D) 2X2 + 7Y ≥ 50 
E) All of the above are valid linear programming constraints.

Question 13

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

Accepted Answer

A) X + Y ≥ 100 and X + Y ≤ 50 
B) X + Y ≥ 15 and X - Y ≤ 10 
C) X + Y ≤ 10 and X ≥ 5 
D) X ≤ 10 and Y ≤ 20 
E) All of the above have a bounded maximum. 
A) X + Y ≥ 100 and X + Y ≤ 50 
B) X + Y ≥ 15 and X - Y ≤ 10 
C) X + Y ≤ 10 and X ≥ 5 
D) X ≤ 10 and Y ≤ 20 
E) All of the above have a bounded maximum.

Question 14

A linear programming problem contains a restriction that reads "the quantity of X must be at least twice as large as the quantity of Y." Formulate this as a linear programming constraint.

Accepted Answer

X ≥ 2Y;alt

Question 15

________ variables allow us to introduce "yes-or-no" decisions into our linear programs and to introduce special logical conditions.

Accepted Answer

The answer of ________ variables allow us to introduce "yes-or-no"...

Question 16

Consider the following constraints from a two-variable linear program: X ≥ 1;Y ≥ 1;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 17

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 18

A linear programming problem contains a restriction that reads "the quantity of S must be no less than one-fourth as large as T and U combined." Formulate this as a linear programming constraint.

Accepted Answer

A) S / (T + U)≥ 4 
B) S - .25T - .25U ≥ 0 
C) 4S ≤ T + U 
D) S ≥ 4T / 4U 
E) S ≥ .25T + S ≥ .25U 
A) S / (T + U)≥ 4 
B) S - .25T - .25U ≥ 0 
C) 4S ≤ T + U 
D) S ≥ 4T / 4U 
E) S ≥ .25T + S ≥ .25U

Question 19

Which of the following is an algorithm for solving linear programming problems of all sizes?

Accepted Answer

A) duplex method 
B) multiplex method 
C) shadow price method 
D) simplex method 
E) decision tree method 
A) duplex method 
B) multiplex method 
C) shadow price method 
D) simplex method 
E) decision tree method

Question 20

A linear programming problem has three constraints,plus nonnegativity constraints on X and Y.The constraints are: 2X + 10Y ≤ 100;4X + 6Y ≤ 120;6X + 3Y ≤ 90. What is the largest quantity of X that can be made without violating any of these constraints?

Accepted Answer

A) 50 
B) 30 
C) 20 
D) 15 
E) 10 
A) 50 
B) 30 
C) 20 
D) 15 
E) 10

Exam 23: Linear Programming

A synonym for shadow price is ________.

Suppose that an iso-profit line is given to be X + Y = 10.Which of the following represents another iso-profit line for the same scenario?

Describe how to incorporate fixed costs into a cost-minimizing linear program,where the fixed cost of using a machine is incurred if any products are produced on that machine.

A linear programming problem contains a restriction that reads "the quantity of Q must be no larger than the sum of R,S,and T." Formulate this as a linear programming constraint.

What is the simplex method?

The ________ is a mathematical expression in linear programming that maximizes or minimizes some quantity.

The optimal solution to a linear programming problem lies within the feasible region.

In which of the following has LP been applied successfully?

Linear programming is an appropriate problem-solving technique for decisions that have no alternative courses of action.

For the constraints given below,which point is in the feasible region of this maximization problem? (1)14x + 6y ≤ 42 (2)x - y ≤ 3 (3)x,y ≥ 0

Which of the following represents a valid constraint in linear programming?

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

A linear programming problem contains a restriction that reads "the quantity of X must be at least twice as large as the quantity of Y." Formulate this as a linear programming constraint.

________ variables allow us to introduce "yes-or-no" decisions into our linear programs and to introduce special logical conditions.

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

An iso-profit line:

A linear programming problem contains a restriction that reads "the quantity of S must be no less than one-fourth as large as T and U combined." Formulate this as a linear programming constraint.

Which of the following is an algorithm for solving linear programming problems of all sizes?

A linear programming problem has three constraints,plus nonnegativity constraints on X and Y.The constraints are: 2X + 10Y ≤ 100;4X + 6Y ≤ 120;6X + 3Y ≤ 90. What is the largest quantity of X that can be made without violating any of these constraints?

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