Question 1

Which of the following is not a requirement of a linear programming problem?

Accepted Answer

A)  an objective function, expressed in terms of linear equations 
B)  constraint equations, expressed as linear equations 
C)  an objective function, to be maximized or minimized 
D)  alternative courses of action 
E)  for each decision variable, there must be one constraint or resource limit 
A)  an objective function, expressed in terms of linear equations 
B)  constraint equations, expressed as linear equations 
C)  an objective function, to be maximized or minimized 
D)  alternative courses of action 
E)  for each decision variable, there must be one constraint or resource limit

Question 2

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

Identify three examples of resources that are typically constrained in a linear programming problem.

Accepted Answer

The textbook gives m

Question 4

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 5

Solving a linear programming problem with the iso-profit line solution method requires that we move the iso-profit line to each corner of the feasible region until the optimum is identified.

Accepted Answer

A) True 
 B)False

Question 6

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. Answer the following questions; base your work on the solution panel provided.
 $\begin{array}{|r|r|r|r|r|r|} 
\hline& \text { A } & \text { B } & &\text { RHS } & \text { Dual } \
\hline \text { Maximize } & 1.5 & 1.5 & \Leftarrow & & \
\hline \text { Molding } & 3. & 2 . & \Leftarrow & 600 & 0.375 \
\hline \text { Painting } & 2. & 4. & \Leftarrow & 600 & 0.1875 \
\hline \text { Packing } & 1. & 3 . & \Leftarrow & 420 & 0. \
\hline \text { Solution }--> & 150 & 75 & & 337.5 &\
\hline
\end{array}$ 
a. What combination of A and B will maximize contribution?
b. What is the maximum possible contribution?
c. Are any resources not fully used up?
 Explain.

Accepted Answer

Maximum contribution occurs at A=150, B=

Question 7

__________ is a mathematical technique designed to help operations managers plan and make decisions relative to the trade-offs necessary to allocate resources.

Accepted Answer

The answer of __________ is a mathematical technique designed to...

Question 8

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

Question 9

A linear programming maximization problem has been solved. In the optimal solution, two resources are scarce. If an added amount could be found for only one of these resources, how would the optimal solution be changed?

Accepted Answer

A)  The shadow price of the added resource will rise. 
B)  The solution stays the same; the extra resource can't be used without more of the other scarce resource. 
C)  The extra resource will cause the value of the objective to fall. 
D)  The optimal mix will be rearranged to use the added resource, and the value of the objective function will rise. 
E)  none of the above 
A)  The shadow price of the added resource will rise. 
B)  The solution stays the same; the extra resource can't be used without more of the other scarce resource. 
C)  The extra resource will cause the value of the objective to fall. 
D)  The optimal mix will be rearranged to use the added resource, and the value of the objective function will rise. 
E)  none of the above

Question 10

Rienzi Farms grows sugar cane and soybeans on its 500 acres of land. An acre of soybeans brings a $1000 contribution to overhead and profit; an acre of sugar cane has a contribution of $2000. Because of a government program no more than 200 acres may be planted in soybeans. During the planting season 1200 hours of planting time will be available. Each acre of soybeans requires 2 hours, while each acre of sugar cane requires 5 hours. The company seeks maximum contribution (profit) from its planting decision.
a. Algebraically state the decision variables, objective and constraints.
b. Plot the constraints
c. Solve graphically, using the corner-point method.

Accepted Answer

The problem statement is contained in th

Question 11

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 12

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.
 $\begin{array}{|l|c|c|c|c|}\hline \text { Cubic feet per } && \text { Weight per } \\text { Item }&\text { unit }&\text { Price per unit }&\text { unit }&\text { Can resell for }\
\hline 2\times4 \text { studs } & 1 & \$ 0.10 & 5 \text { pounds } & \$ 0.80 \
\hline 4 \times 8 \text { plywood } & 3 & \$ 0.50 & 20 \text { pounds } & \$ 3.00 \
\hline \text { Concrete blocks } & 0.5 & \$ 0.25 & 10 \text { pounds } & \$ 0.75 \
\hline
\end{array}$ 
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 13

In linear programming, a statement such as "maximize contribution" becomes an objective function when the problem is formulated.

Accepted Answer

A) True 
 B)False

Question 14

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

Accepted Answer

A) True 
 B)False

Question 15

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 16

A linear programming problem contains a restriction that reads "the quantity of S must be no more than one-fourth as large as T and U combined." Formulate this as a constraint ready for use in problem solving software.

Accepted Answer

The quoted sentence translates into the

Question 17

A linear programming problem contains a restriction that reads "the quantity of Q must be at least as large as the sum of R, S, and T." Formulate this as a constraint ready for use in problem solving software.

Accepted Answer

The quoted sentence translates into the

Question 18

What is the feasible region in a linear programming problem?

Accepted Answer

The feasible region

Question 19

What is linear programming?

Accepted Answer

Linear programming is a mathem

Question 20

A linear programming problem has three constraints: 2X + 10Y ≤ 1004X + 6Y ≤ 1206X + 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 22: Linear Programming

Which of the following is not a requirement of a linear programming problem?

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

Identify three examples of resources that are typically constrained in a linear programming problem.

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?

Solving a linear programming problem with the iso-profit line solution method requires that we move the iso-profit line to each corner of the feasible region until the optimum is identified.

__________ is a mathematical technique designed to help operations managers plan and make decisions relative to the trade-offs necessary to allocate resources.

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

A linear programming maximization problem has been solved. In the optimal solution, two resources are scarce. If an added amount could be found for only one of these resources, how would the optimal solution be changed?

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.

In linear programming, a statement such as "maximize contribution" becomes an objective function when the problem is formulated.

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

A linear programming problem contains a restriction that reads "the quantity of S must be no more than one-fourth as large as T and U combined." Formulate this as a constraint ready for use in problem solving software.

A linear programming problem contains a restriction that reads "the quantity of Q must be at least as large as the sum of R, S, and T." Formulate this as a constraint ready for use in problem solving software.

What is the feasible region in a linear programming problem?

What is linear programming?

A linear programming problem has three constraints: 2X + 10Y ≤ 1004X + 6Y ≤ 1206X + 3Y ≥ 90 What is the largest quantity of X that can be made without violating any of these constraints?

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