Question 1

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

Accepted Answer

A) True 
 B)False  True

Question 2

A firm makes two products, Y and Z. Each unit of Y costs $10 and sells for $40. Each unit of Z costs $5 and sells for $25. If the firm's goal were to maximize profit, the appropriate objective function would be

Accepted Answer

A)  maximize $40Y = $25Z 
B)  maximize $40Y + $25Z 
C)  maximize $30Y + $20Z 
D)  maximize 0.25Y + 0.20Z 
E)  none of the above 
A)  maximize $40Y = $25Z 
B)  maximize $40Y + $25Z 
C)  maximize $30Y + $20Z 
D)  maximize 0.25Y + 0.20Z 
E)  none of the above C

Question 3

Suppose that a chemical manufacturer is deciding how to mix two chemicals, A and B. A costs $5/gram and B costs $4/gram if they are ordered above the current supply level. There are currently 40 grams of A and 30 grams of B that must be used in the mix or they will expire. If a customer wants 1 kg of the mix with at least 40% A but no more than 55% A, how many grams of each chemical should be included in the mix?

Accepted Answer

Students should start by using all of the A and B supplies on hand. This totals 70grams and means that 930 grams will need to be ordered. A must have between 400 and 550 grams while B will be 1000-A grams. Removing the already assigned supplies gives that
A (ordered) between 360 and 510
B(ordered) = 930-A => A+B=930
Students should then recognize that the corner points lie where A=360 (ordered), B=570 (ordered) and A = 510 (ordered) and B = 420 (ordered). Using the corner-point approach, the total cost will be minimized at one of these two locations.
TC(A=360 ordered) = 360*5+570*4 = $4080
TC(A=510 ordered) = 510*5+420*4 = $4230
Thus the manufacturer should order 360 grams of A and 570 grams of B. Mixing these ordered supplies with the on hand inventory (treated as being free since it will expire) would give a mix of 400 grams of A and 600 grams of B.

Question 4

In linear programming, if there are three constraints, each representing a resource that can be used up, the optimal solution must use up all of each of the three resources.

Accepted Answer

A) True 
 B)False

Question 5

A stereo mail order center has 8,000 cubic feet available for storage of its private label loudspeakers. The ZAR-3 speakers cost $295 each and require 4 cubic feet of space; the ZAR-2ax speakers cost $110 each and require 3 cubic feet of space; and the ZAR-4 model costs $58 and requires 1 cubic foot of space. The demand for the ZAR-3 is at most 20 units per month. The wholesaler has $100,000 to spend on loudspeakers this month. Each ZAR-3 contributes $105, each ZAR-2ax contributes $50, and each ZAR-4 contributes $28. The objective is to maximize total contribution. Write out the objective and the constraints.

Accepted Answer

The objective is to maximize 105 ZAR-3 +

Question 6

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 7

Linear programming helps operations managers make decisions necessary to make effective use of resources such as machinery, labor, money, time, and raw materials.

Accepted Answer

A) True 
 B)False

Question 8

What combination of x and y will yield the optimum for this problem? Maximize $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 9

The difference between minimization and maximization problems is that

Accepted Answer

A)  minimization problems cannot be solved with the corner-point method 
B)  maximization problems often have unbounded regions 
C)  minimization problems often have unbounded regions 
D)  minimization problems cannot have shadow prices 
E)  None of the above are true. 
A)  minimization problems cannot be solved with the corner-point method 
B)  maximization problems often have unbounded regions 
C)  minimization problems often have unbounded regions 
D)  minimization problems cannot have shadow prices 
E)  None of the above are true.

Question 10

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 constraint ready for use in problem solving software.

Accepted Answer

A)  S / (T + U) ≥ 4 
B)  S - .25T -.25U ≥ 0 
C)  4S ≤ T + U 
D)  S ≥ 4T / 4U 
E)  none of the above 
A)  S / (T + U) ≥ 4 
B)  S - .25T -.25U ≥ 0 
C)  4S ≤ T + U 
D)  S ≥ 4T / 4U 
E)  none of the above

Question 11

In linear programming, statements such as "the blend must consist of at least 10% of ingredient A, at least 30% of ingredient B, and no more than 50% of ingredient C" can be made into valid constraints even though the percentages do not add up to 100 percent.

Accepted Answer

A) True 
 B)False

Question 12

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 13

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 14

A linear programming problem contains a restriction that reads "the quantity of X must be at least three times as large as the quantity of Y." Which of the following inequalities is the proper formulation of this constraint?

Accepted Answer

A)  3X ≥ Y 
B)  X ≤ 3Y 
C)  X + Y≥3 
D)  X - 3Y ≥ 0 
E)  3X ≤ Y 
A)  3X ≥ Y 
B)  X ≤ 3Y 
C)  X + Y≥3 
D)  X - 3Y ≥ 0 
E)  3X ≤ Y

Question 15

Tom is a habitual shopper at garage sales. Last Saturday he stopped at one where there were several types of used building materials for sale. At the low prices being asked, Tom knew that he could resell the items in another town for a substantial gain. Four things stood in his way: he could only make one round trip to resell the goods; his pickup truck bed would hold only 1000 pounds; the pickup truck bed could hold at most 70 cubic feet of merchandise; and he had only $200 cash with him. He wants to load his truck with the mix of materials that will yield the greatest profit when he resells them.
   State the decision variables (give them labels). State the objective function. Formulate the constraints of this problem. DO NOT SOLVE, but speculate on what might be a good solution for Tom. You must supply a set of quantities for the decision variables. Provide a sentence or two of support for your choice.

Accepted Answer

Student responses must be feasible, but

Question 16

The region that satisfies the constraint 4X + 15Z ≥ 1000 includes the origin of the graph.

Accepted Answer

A) True 
 B)False

Question 17

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 18

The objective of a linear programming problem is to maximize 1.50A + 1.50B, subject to 3A + 2B ≤ 600, 2A + 4B ≤ 600, and 1A + 3B ≤ 420.
a. Plot the constraints on the grid below
c. Identify the feasible region and its corner points. Show your work.
d. What is the optimal product mix for this problem?

Accepted Answer

The objective of the problem is to maxim

Question 19

In sensitivity analysis, a zero shadow price (or dual value) for a resource ordinarily means that the resource has not been used up.

Accepted Answer

A) True 
 B)False

Question 20

In linear programming, a statement such as "maximize contribution" becomes a(n)

Accepted Answer

A)  constraint 
B)  slack variable 
C)  objective function 
D)  violation of linearity 
E)  decision variable 
A)  constraint 
B)  slack variable 
C)  objective function 
D)  violation of linearity 
E)  decision variable

Exam 19: Acceptance Sampling

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

A firm makes two products, Y and Z. Each unit of Y costs $10 and sells for $40. Each unit of Z costs $5 and sells for $25. If the firm's goal were to maximize profit, the appropriate objective function would be

In linear programming, if there are three constraints, each representing a resource that can be used up, the optimal solution must use up all of each of the three resources.

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

Linear programming helps operations managers make decisions necessary to make effective use of resources such as machinery, labor, money, time, and raw materials.

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

The difference between minimization and maximization problems is that

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 constraint ready for use in problem solving software.

In linear programming, statements such as "the blend must consist of at least 10% of ingredient A, at least 30% of ingredient B, and no more than 50% of ingredient C" can be made into valid constraints even though the percentages do not add up to 100 percent.

In which of the following has LP been applied successfully?

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

A linear programming problem contains a restriction that reads "the quantity of X must be at least three times as large as the quantity of Y." Which of the following inequalities is the proper formulation of this constraint?

The region that satisfies the constraint 4X + 15Z ≥ 1000 includes the origin of the graph.

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

In sensitivity analysis, a zero shadow price (or dual value) for a resource ordinarily means that the resource has not been used up.

In linear programming, a statement such as "maximize contribution" becomes a(n)

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