8.
Refer to
Figure 3.14, which shows the computer solution of Problem 7.
a. How much would the return for U.S. Oil have to
increase before it would be beneficial to increase the investment in this
stock?
b.
How much
would the return for Huber steel have to decrease before it would be beneficial
to reduce the investment in this tock?
c.
How much
would the total annual return be reduced if the U.S. Oil maximum were reduced
to 900 shares?
Quantitative
Analysis BA 452 Homework 3 Questions
9.
Recall the
Tom’s, Inc., problem (Chapter 2, Problem 28). Letting
W=jars of western Foods Salsa
M=jars of Mexico City Salsa
Leads to the formulation:
_{. .} 1 +
1.25 5 + 7 ? 4480 ?
3 + 1 ? 2080 2 + 2 ? 1600 , ? 0
The computer solution is shown in Figure 3.15.
a. What is the optimal solution, and what are the
optimal production quantities?
b. Specify the objective function ranges.
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c. What are the dual values for each constraint?
Interpret each.
d. Identify each of the righthandside ranges.
Quantitative
Analysis BA 452 Homework 3 Questions
10.
Recall the
Innis Investments problem (Chapter 2, Problem 39). Letting

S=units purchased in the stock fund


M=units purchased in the
money market fund

leads to the
following formulation:



8
+ 3


. .

50
+ 100 ? 1,200,000


5
+ 4 ? 60,000



? 3,000



,
? 0


The computer solution is shown in Figure 3.16.
a. What is the optimal solution, and what is the
minimum total risk?
b. Specify the objective coefficient ranges.
c. How much annual income will be earned by the
portfolio?
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d. What is the rate of return for the portfolio?
e. What is the dual value for the funds available
constraint?
Quantitative
Analysis BA 452 Homework 3 Questions
f.
What is the
marginal rate of return on extra funds added to the portfolio?
11.
Refer to
Problem 10 and the computer solution shown in Figure 3.16.
a.
Suppose the
risk index for the stock fund (the value of Cs) increases from its current
value of 8 to 12. How does the optimal solution change, if at all?
b.
Suppose the
risk index for the money market fund (the value of Cm) increases from its
current value of 3 to 3.5. how does the optimal solution change, if at all?
c.
Suppose Cs
increases to 12 and Cm increases to 3.5. How does the optimal solution change,
if at all?
12.
Quality Air
conditioning manufactures three hoe air conditioners: an economy model, a
standard model, and a deluxe model. The profits per unit are $63, $95, and
$135, respectively. The production requirements per unit are as follows:

Number of

Number of

Manufacturing


Fans

Cooling Coils

Time(hours)

Economy

1

1

8

Standard

1

2

12

Deluxe

1

4

14





For the coming production period, the company has
200 fan motors, 320 cooling coils, and 2400 hours of manufacturing time
available. How many economy models (E), standard models (S), and deluxe models
(D) should the company produce in order to maximize profit? The linear
programming model for the problem is as follows:
63 + 95
+ 135




. .

1
+ 1 + 1 ? 200

Fan motors



Cooling coils



1 + 2 +
4 ? 320


Manufacturing time



8
+ 12 + 14 ? 2400




,
, ? 0




The computer solution is shown in Figure 3.17.
a. What is the optimal solution, and what is the
value of the objective function
b. Which constraints are binding?
c. Which constraint shows extra capacity? How much?
d.
If the
profit for the deluxe model were increased to $150 per unit, would the optimal
solution change? Use the information in Figure 3.17 to answer this question.
Quantitative
Analysis BA 452 Homework 3 Questions
13.
Refer to
the computer solution of Problem 12 in Figure 3.17
a. Identify the range of optimality for each
objective function coefficient.
b.
Suppose the
profit for the economy model is increased by $6 per unit, the profit for the
standard model is decreased by 42 per unit, and the profit for the deluxe model
is increased by $4 per unit. What will the new optimal solution be?
c. Identify the range of feasibility for the
righthandside values.
d. If the number of fan motor available for
production is increased by 100, will the dual value for that constraint change?
Explain.
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