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Question # 00005214
Subject: Mathematics
Due on: 12/30/2013
Posted On: 12/12/2013 11:51 AM

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Homework 3 Supplemented Questions


1. Consider the following linear program:

. .


3 + 2

1 + 1 ? 10

3 + 1 ? 24

1 + 2 ? 16 , ? 0


a. Use the graphical solution procedure to find the optimal solution.

b. Assume that the objective function coefficient for A changes from 3 to 5. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution.

c. Assume that the objective function coefficient for A remains 3, but the objective function coefficient for B changes from 2 to 4. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution.

d. The computer solution for the linear program in part (a) provides the following objective coefficient range information:

Objective

Allowable

Allowable

Variable

Coefficient

Increase

Decrease

A

3.00000

3.00000

1.00000

B

2.00000

1.00000

1.00000

Use this objective coefficient range information to answer parts (b) and (c)


Quantitative Analysis BA 452 Homework 3 Questions

2. Consider the linear program in Problem 1. The value of the optimal solution is 27. Suppose that the right-hand side for constraint 1 is increased from 10 to 11.

a. Use the graphical solution procedure to find the new optimal solution.

b. Use the solution to part (a) to determine the dual value or constraint 1.

c. The computer solution for the linear program in Problem 1 provides the following right-hand-side range information:

RHS

Allowable

Allowable

Constraint

Value

Increase

Decrease

1

10.00000

1.20000

2.00000

2

24.00000

6.00000

6.00000

3

16.00000

Infinite

3.00000

d. The dual value for constraint 2 is 0.5. Using this dual value and the right-hand-side range information in part (c), what conclusion can be drawn about the effect of changes to the right-hand side of constraint 2?


Quantitative Analysis BA 452 Homework 3 Questions

3. Consider the following linear program:

Min

8X + 12Y

s.t.

1X

+ 3Y

? 9

2X

+ 2Y

? 10

6X

+ 2Y

? 18

A, B ? 0

a. Use the graphical solution procedure to find the optimal solution.

b. Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution.

c. Assume that the objective function coefficient for S remains 8, but the objective function coefficient for Y changes from 12 to 6. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution.

d. The computer solution for the linear program in part (a) provides the following objective coefficient range information:

Objective

Allowable

Allowable

Variable

Coefficient

Increase

Decrease

X

8.00000

4.00000

4.00000

Y

12.00000

12.00000

4.00000

How would this objective coefficient range information help you answer parts (b) and (c) prior to re-solving the problem?


Quantitative Analysis BA 452 Homework 3 Questions

4. Consider the linear program in Problem 3. The value of the optimal solution is 48. Suppose that the right-hand side for constraint 1 is increased from 9 to 10.

a. Use the graphical solution procedure to find the new optimal solution.

b. Use the solution to part (a) to determine the dual value for constraint 1.

c. The computer solution for the linear program in Problem 3 provides the following right-hand-side range information:

RHS

Allowable

Allowable

Constraint

Value

Increase

Decrease

1

9.00000

2.00000

4.00000

2

10.00000

8.00000

1.00000

3

18.00000

4.00000

Infinite

What does the right-hand-side range information for constraint 1 tell you about the dual value for constraint 1?

d. The dual value for constraint 2 is 3. Using this dual value and the right-hand-side range information in part (c), what conclusion can be drawn about the effect of changes to the right-hand side of constraint 2?


Quantitative Analysis BA 452 Homework 3 Questions

5. Refer to the Kelson Sporting Equipment problem (Chapter 2, Problem 24). Letting

R=number of regular gloves C=number of catcher’s mitts

Leads to the following formulation:

5 + 8 . .

+?32? ? 900?12?+?13? ?300 ?

?18? +?14? ? 100 ? ,? 0

The computer solution is shown I Figure 3.13.


Quantitative Analysis BA 452 Homework 3 Questions

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a. What is the optimal solution, and what is the value of the total profit contribution?

b. Which constraints are binding?

c. What are the dual values for the resources? Interpret each.

d. If overtime can be scheduled in one of the departments, where would you recommend doing so?

6. Refer to the computer solution of the Kelson Sporting Equipment problem in Figure 3.13 (see Problem 5).

a. Determine the objective coefficient ranges.

b. Interpret the ranges in part (a).

c. Interpret the right-hand-sides ranges.

d. How much will the value of the optimal solution improve if 20 extra hours of packaging and shipping time are made available?


Quantitative Analysis BA 452 Homework 3 Questions

7. Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A particular portfolio consists of U shares of U.S. Oil and H shares of Huber Steel. The annual return for U.S. Oil is $3 per share and the annual return for Huber Steel is $5 per share. U.S. Oil sells for $25 per share and Huber Steel sells for $50 per share. The portfolio has $80,000 to be invested. The

portfolio risk index (.50 per share of U.S. Oil and 0.25 per share for Huber Steel) has a maximum of 700. In addition, the portfolio is limited to a maximum of 1000 shares of U.S. Oil. The linear

programming formulation that will maximize the total annual return of the portfolio is as follows:

3 +

5

. .

25 +

50 ? 80,000

0.50 + 0.25 ?

700

1

? 0

?

1000

. .

,

The computer solution of this problem is shown in Figure 3.14.

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Quantitative Analysis BA 452 Homework 3 Questions

a. What is the optimal solution, and what is the value of the total annual return?

b. Which constraints are binding? What is your interpretation of these constraints in terms of the problem?

c. What are the dual values for the constraints? Interpret each.

d. Would it be beneficial to increase the maximum amount invested in U.S. Oil? Why or why not?

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Tutorial Preview …dual xxxxx is x c The xxxxxxxxxx side range xxx constraint x xx 5 xx 11 As xxxx as the xxxxxxxxxx side xxxxx xxxxxx this xxxxxx the dual xxxxx of 2 xx applicable xxxxx xxxxxxxxxx the xxxxxxxxxx side does xxx improve the xxxxx of xxx xxxxxxx solution, xxxxxxxxxx the right-hand xxxx of constraint x would x xxxxxxxxx d xx long as xxx right-hand side xx constraint x xx between x and 18, x unit increase xx the xxxxxxxxxx xxxx will xxxxx the value xx the optimal xxxxxxxx to xxxxxxxx xx 3 x a Regular xxxxx = 500 xxxxxxxxxxx Mitt x xxx Value x 3700 b xxx finishing and xxxxxxxxx and xxxxxxxx xxxxxxxxxxx are xxxxxxx c Cutting xxx Sewing = x Finishing x x Packaging xxx Shipping = xx Additional finishing xxxx is xxxxx xx per xxxx and additional xxxxxxxxx and shipping xxxx is xxxxx xxx per xxxx d In xxx packaging and xxxxxxxx department xxxx…
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Preview: value xx the xxxxxxx solution has xxxxxxxxx by 50 x 48 x x Thus, xxx dual value xx 2 The xxxxxxxxxx side xxxxx xxx constraint x is 5 xx 11 As xxxx as xxx xxxxxxxxxx side xxxxx within this xxxxxx the dual xxxxx of x xx applicable xxxxx increasing the xxxxxxxxxx side does xxx improve xxx xxxxx of xxx optimal solution, xxxxxxxxxx the right-hand xxxx of xxxxxxxxxx x would x desirable As xxxx as the xxxxxxxxxx side xx xxxxxxxxxx 2 xx between 9 xxx 18, a xxxx increase xx xxx right-hand xxxx will cause xxx value of xxx optimal xxxxxxxx xx increase xx 3 a xxxxxxx Glove = xxx Catcher’s xxxx x 150 xxxxx = 3700 xxx finishing and xxxxxxxxx and xxxxxxxx xxxxxxxxxxx are xxxxxxx Cutting and xxxxxx = 0 xxxxxxxxx = x xxxxxxxxx and xxxxxxxx = 28 xxxxxxxxxx finishing time xx worth xx.....
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