Question 1

What is sensitivity analysis?

Accepted Answer

Sensitivity analysis projects how much a solution might change if there were changes in the variables or input data.

Question 2

A financial advisor is about to build an investment portfolio for a client who has $100,000 to invest. The four investments available are A, B, C, and D. Investment A will earn 4 percent and has a risk of one "point" per $1,000 invested. B earns 6 percent with 2 risk points; C earns 9 percent with 6 risk points; and D earns 11 percent with a risk of 8. The client has put the following conditions on the investments: A is to be no more than one-third of the total invested. A cannot be less than 10 percent of the total investment. D cannot be more than C. Total risk points must be at or below 1,000. Let A be the amount invested in investment A, and define B, C, and D similarly. Formulate the linear programming model.

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Question 2

Correct Answer:

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Maximize return = 0.04A + 0.06B + 0.09C + 0.11D
Subject to
A + B + C + D = $100,000
.67A - .33B - .33C - .33D ≤ 0 (rearranged from A ≤ .33(A + B + C + D))
.9A - .1B - .1C - .1D ≥ 0 (rearranged from A ≥ .1 (A + B + C + D))
-C + D ≤ 0 (rearranged from D ≤ C)
.001A + .002B + .006C + .008C ≤ 1000
A, B, C, D ≥ 0

Accepted Answer

Maximize return = 0.04A + 0.06B + 0.09C + 0.11D
Subject to
A + B + C + D = $100,000
.67A - .33B - .33C - .33D ≤ 0 (rearranged from A ≤ .33(A + B + C + D))
.9A - .1B - .1C - .1D ≥ 0 (rearranged from A ≥ .1 (A + B + C + D))
-C + D ≤ 0 (rearranged from D ≤ C)
.001A + .002B + .006C + .008C ≤ 1000
A, B, C, D ≥ 0

Question 3

________ is an analysis that projects how much a solution might change if there were changes in the variables or input data.

Accepted Answer

Sensitivity analysis

Question 4

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, three minutes for painting, and two minutes per unit for packing. There will be 600 minutes available for molding, 600 minutes for painting, and 480 minutes for packing. Both products have contributions of $1.50 per unit. Answer the following questions; base your work on the solution panel provided.
   (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

(a) Maximum contribution occurs at A = 1

Question 5

The ________ is the set of all feasible combinations of the decision variables.

Accepted Answer

The answer of The ________ is the set of all...

Question 6

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, what would be the appropriate objective function?

Accepted Answer

A)  Maximize profit = $40Y = $25Z 
B)  Maximize profit = $40Y + $25Z 
C)  Maximize profit = $30Y + $20Z 
D)  Maximize profit = 0.25Y + 0.20Z 
E)  Maximize profit = $50(Y + Z) 
A)  Maximize profit = $40Y = $25Z 
B)  Maximize profit = $40Y + $25Z 
C)  Maximize profit = $30Y + $20Z 
D)  Maximize profit = 0.25Y + 0.20Z 
E)  Maximize profit = $50(Y + Z)

Question 7

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

Accepted Answer

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

Question 8

Capital Co. is considering 5 different projects. Define Xi as a binary variable that equals 1 if project i is undertaken and 0 otherwise, for i = 1, 2, 3, 4, 5. Which of the following represents the constraint(s) stating that projects 2, 3, and 4 cannot all three be undertaken simultaneously?

Accepted Answer

A)  X2 + X3 + X4 ≤ 3 
B)  X1 + X2 + X3 + X4 + X5 ≤ 3 
C)  X2 + X3 + X4 ≤ 1 
D)  X2 + X3 + X4 ≤ 2 
E)  X2 + X3 ≤ 1 and X3 + X4 ≤ 1 
A)  X2 + X3 + X4 ≤ 3 
B)  X1 + X2 + X3 + X4 + X5 ≤ 3 
C)  X2 + X3 + X4 ≤ 1 
D)  X2 + X3 + X4 ≤ 2 
E)  X2 + X3 ≤ 1 and X3 + X4 ≤ 1

Question 9

The graphical method of solving linear programs can handle only maximization problems.

Accepted Answer

A) True 
 B)False

Question 10

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

Accepted Answer

A) True 
 B)False

Question 11

What is the feasible region in a linear programming problem?

Accepted Answer

The feasible region

Question 12

What are corner points? What is their relevance to solving linear programming problems?

Accepted Answer

Corner points are the intersections of t

Question 13

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 300 acres may be planted in soybeans. During the planting season 1500 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. What is the optimal solution?

Accepted Answer

A)  300 acres of soybeans, 180 acres of sugar cane 
B)  300 acres of soybeans, 200 acres of sugar cane 
C)  0 acres of soybeans, 300 acres of sugar cane 
D)  500 acres of soybeans, 0 acres of sugar cane 
E)  300 acres of soybeans, 100 acres of sugar cane 
A)  300 acres of soybeans, 180 acres of sugar cane 
B)  300 acres of soybeans, 200 acres of sugar cane 
C)  0 acres of soybeans, 300 acres of sugar cane 
D)  500 acres of soybeans, 0 acres of sugar cane 
E)  300 acres of soybeans, 100 acres of sugar cane

Question 14

A maximizing linear programming problem has two constraints: 2X + 4Y ≤ 100 and 3X + 10Y ≤ 210, in addition to constraints stating that both X and Y must be nonnegative. What are the corner points of the feasible region of this problem?

Accepted Answer

A)  (0, 0), (50, 0), (0, 21), and (20, 15) 
B)  (0, 0), (70, 0), (25, 0), and (15, 20) 
C)  (20, 15) 
D)  (0, 0), (0, 100), and (210, 0) 
E)  (0, 0), (0, 25), (50, 0), (0, 21), and (70, 0) 
A)  (0, 0), (50, 0), (0, 21), and (20, 15) 
B)  (0, 0), (70, 0), (25, 0), and (15, 20) 
C)  (20, 15) 
D)  (0, 0), (0, 100), and (210, 0) 
E)  (0, 0), (0, 25), (50, 0), (0, 21), and (70, 0)

Question 15

Binary variables can only take on the values of 1 or 2.

Accepted Answer

A) True 
 B)False

Question 16

In the graphical solution to a linear program, the region that satisfies the constraint 4X + 15Z ≤ 1000 includes the origin of the graph.

Accepted Answer

A) True 
 B)False

Question 17

A feedlot is trying to decide on the lowest cost mix that will still provide adequate nutrition for its cattle. Suppose that the numbers in the chart represent the number of grams of ingredient per 100 grams of feed and that the cost of Feed X is $5/100grams, Feed Y is $3/100 grams, and Feed X is $8/100 grams. Each cow will need 50 grams of A per day, 20 grams of B, 30 grams of C, and 10 grams of D. The feedlot can get no more than 200 grams per day per cow of any of the feed types. Formulate the problem as a linear program.

Accepted Answer

Let X, Y, Z be number of grams of each r

Question 18

Two methods of conducting sensitivity analysis on solved linear programming problems are ________ and ________.

Accepted Answer

trial and error, the

Question 19

A shadow price (or dual value) reflects which of the following in a maximization problem?

Accepted Answer

A)  the marginal gain in the objective realized by subtracting one unit of a resource 
B)  the market price that must be paid to obtain additional resources 
C)  the increase in profit that would accompany one added unit of a scarce resource 
D)  the reduction in cost that would accompany a one unit decrease in the resource 
E)  the profit contribution necessary for that item to be included in the optimal solution 
A)  the marginal gain in the objective realized by subtracting one unit of a resource 
B)  the market price that must be paid to obtain additional resources 
C)  the increase in profit that would accompany one added unit of a scarce resource 
D)  the reduction in cost that would accompany a one unit decrease in the resource 
E)  the profit contribution necessary for that item to be included in the optimal solution

Question 20

Constraints are needed to solve linear programming problems by hand, but not by computer.

Accepted Answer

A) True 
 B)False

What is sensitivity analysis?

________ is an analysis that projects how much a solution might change if there were changes in the variables or input data.

The ________ is the set of all feasible combinations of the decision variables.

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, what would be the appropriate objective function?

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

Capital Co. is considering 5 different projects. Define X_i as a binary variable that equals 1 if project i is undertaken and 0 otherwise, for i = 1, 2, 3, 4, 5. Which of the following represents the constraint(s) stating that projects 2, 3, and 4 cannot all three be undertaken simultaneously?

The graphical method of solving linear programs can handle only maximization problems.

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

What is the feasible region in a linear programming problem?

What are corner points? What is their relevance to solving linear programming problems?

A maximizing linear programming problem has two constraints: 2X + 4Y ≤ 100 and 3X + 10Y ≤ 210, in addition to constraints stating that both X and Y must be nonnegative. What are the corner points of the feasible region of this problem?

Binary variables can only take on the values of 1 or 2.

In the graphical solution to a linear program, the region that satisfies the constraint 4X + 15Z ≤ 1000 includes the origin of the graph.

Two methods of conducting sensitivity analysis on solved linear programming problems are and .

A shadow price (or dual value) reflects which of the following in a maximization problem?

Constraints are needed to solve linear programming problems by hand, but not by computer.

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Exam 18: Linear Programming

What is sensitivity analysis?

________ is an analysis that projects how much a solution might change if there were changes in the variables or input data.

The ________ is the set of all feasible combinations of the decision variables.

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, what would be the appropriate objective function?

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

Capital Co. is considering 5 different projects. Define Xi as a binary variable that equals 1 if project i is undertaken and 0 otherwise, for i = 1, 2, 3, 4, 5. Which of the following represents the constraint(s) stating that projects 2, 3, and 4 cannot all three be undertaken simultaneously?

The graphical method of solving linear programs can handle only maximization problems.

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

What is the feasible region in a linear programming problem?

What are corner points? What is their relevance to solving linear programming problems?

A maximizing linear programming problem has two constraints: 2X + 4Y ≤ 100 and 3X + 10Y ≤ 210, in addition to constraints stating that both X and Y must be nonnegative. What are the corner points of the feasible region of this problem?

Binary variables can only take on the values of 1 or 2.

In the graphical solution to a linear program, the region that satisfies the constraint 4X + 15Z ≤ 1000 includes the origin of the graph.

Two methods of conducting sensitivity analysis on solved linear programming problems are ________ and ________.

A shadow price (or dual value) reflects which of the following in a maximization problem?

Constraints are needed to solve linear programming problems by hand, but not by computer.

Operations and Productivity

Operations Strategy in a Global Environment

Project Management

Forecasting

Design of Goods and Services

Managing Quality

Process Strategies

Location Strategies

Human Resources, Job Design, and Work Measurement

Supply Chain Management

Inventory Management

Aggregate Planning and Sop

Material Requirements Planning Mrp and Erp

Short-Term Scheduling

Lean Operations

Maintenance and Reliability

Decision-Making Tools

Transportation Models

Waiting-Line Models

Learning Curves

Simulation

Applying Analytics to Big Data in Operations Management

Filters

Capital Co. is considering 5 different projects. Define X_i as a binary variable that equals 1 if project i is undertaken and 0 otherwise, for i = 1, 2, 3, 4, 5. Which of the following represents the constraint(s) stating that projects 2, 3, and 4 cannot all three be undertaken simultaneously?

Two methods of conducting sensitivity analysis on solved linear programming problems are and .