Question 1

Suppose that a maximization LP problem has corners of (0,0), (5,0), and (0,5). How many possible combinations of X and Y will yield the maximum profit if profit is given to be 5X + 5Y?

Accepted Answer

A)  0 
B)  1 
C)  2 
D)  5 
E)  Infinite

Question 2

John's Locomotive Works manufactures a model locomotive. It comes in two versions-a standard (X1), and a deluxe (X2). The standard version generates $250 per locomotive for the standard version, and $350 per locomotive for the deluxe version. One constraint on John's production is labour hours. He only has 40 hours per week for assembly. The standard version requires 250 minutes each, while the deluxe requires 350 minutes. John's milling machine is also a limitation. There are only 20 hours a week available for the milling machine. The standard unit requires 60 minutes, while the deluxe requires 120. Formulate as a linear programming problem, and solve using either the graphical or corner points solution method.

Accepted Answer

The answer of John's Locomotive Works manufactures a model locomotive....

Question 3

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)  The extra resource will cause the value of the objective to rise.

Question 4

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.

Question 5

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

Question 6

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
b. Identify the feasible region and its corner points. Show your work.
c. What is the optimal product mix for this problem?

Accepted Answer

The answer of The objective of a linear programming problem...

Question 7

What is linear programming?

Accepted Answer

The answer of What is linear programming?...

Question 8

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

Question 9

What is sensitivity analysis?

Accepted Answer

The answer of What is sensitivity analysis?...

Question 10

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.

Question 11

The region that satisfies all of the constraints in graphical linear programming is called the region of optimality.

Accepted Answer

A) True 
 B)False

Question 12

A linear programming problem has two constraints 2X + 4Y = 100 and 1X + 8Y ≤ 100, plus non-negativity constraints on X and Y. Which of the following statements about its feasible region is true?

Accepted Answer

A)  The points (100, 0) and (0, 25) both lie outside the feasible region. 
B)  The two corner points are (33-1/3, 8-1/3) and (50, 0). 
C)  The graphical origin (0, 0) is not in the feasible region. 
D)  The feasible region is a straight line segment, not an area. 
E)  All of the above are true.

Question 13

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

The answer of Tom is a habitual shopper at garage...

Question 14

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 labour 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 15

What is the usefulness of a shadow price (or dual value)?

Accepted Answer

The answer of What is the usefulness of a shadow...

Question 16

A company has the following usage of inputs, constraints on inputs and profit margins to make their three products.
 $$\begin{array} { l l l l l } 
\text { Product } & \text { Wiring } & \text { Drilling } & \text { Assembly } & \text { Profit } \
\text { X202 } & 0.6 & 0.41 & 0.8 & 14 \
\text { Y303 } & 0.1 & 0.57 & 0.47 & 9.75 \
\text { Z404 } & 0.35 & 0.3 & 0.26 & 12.25
\end{array}$$ There are maximum amounts of the following: 1625 hours for wiring, 1750 hours for drilling and 1175 hours for Assembly. Make sure that the units produced are integers. Solve for the above problem.
a) How many units of each product will be made?
b) What is the maximum profit?
c) Which input has the most amount of slack?

Accepted Answer

The answer of A company has the following usage of...

Question 17

________ are restrictions that limit the degree to which a manager can pursue an objective.

Accepted Answer

The answer of ________ are restrictions that limit the degree...

Question 18

Explain how to use the iso-profit line in a graphical maximization problem.

Accepted Answer

The answer of Explain how to use the iso-profit line...

Question 19

Suppose an LP problem was subject to constraints of
2X + Y> 10
X + 3Y> 20
Suppose that a new constraint is added, of the form 3X + A ∗ Y> 90. What is the largest value that A can have so that this new constraint is redundant?

Accepted Answer

The answer of Suppose an LP problem was subject to...

Question 20

In terms of linear programming, the fact that the solution is infeasible implies that the "profit" can increase without limit.

Accepted Answer