Page 296 -

276 CHAPTER 6 SIMPLEX-BASED SENSITIVITY ANALYSIS AND DUALITY

c. If the profit contribution per deluxe bag drops to E7 per unit, how will the optimal
solution be affected?
d. What unit profit contribution would be necessary for the deluxe bag before the company
would consider changing its current production plan?
e. If the profit contribution of the deluxe bags can be increased to E15 per unit, what is the
optimal production plan? State what you think will happen before you compute the new
optimal solution.
7 For Problem 6:
a. Calculate the range of feasibility for b 1 (cutting and dyeing capacity).
b. Calculate the range of feasibility for b 2 (sewing capacity).
c. Calculate the range of feasibility for b 3 (finishing capacity).
d. Calculate the range of feasibility for b 4 (inspection and packaging capacity).
e. Which of thesefour departments would you beinterested in scheduling for overtime? Explain.
4
8 a. Calculate the final simplex tableau for Problem 6 after increasing b 1 from 630 to 682 / 11 .
b. Would the current basis be optimal if b 1 were increased further? If not, what would be
the new optimal basis?
9 For Problem 6:
a. How much would profit increase if an additional 30 hours became available in the
cutting and dyeing department (i.e., if b 1 were increased from 630 to 660)?
b. How much would profit decrease if 40 hours were removed from the sewing department?
c. How much would profit decrease if, because of an employee accident, only 570 hours
instead of 630 were available in the cutting and dyeing department?
10 The following are additional conditions encountered by GulfGolf (Problem 6).
a. Suppose because of some new machinery the company was able to make a small
reduction in the amount of time it took to do the cutting and dyeing (constraint 1) for
a standard bag. What effect would this reduction have on the objective function?
b. Management believes that by buying a new sewing machine, the sewing time for
standard bags can be reduced from 0.5 to 0.3333 hour. Do you think this machine
would be a good investment? Why?
11 Innis Investments manages funds for a number of companies and wealthy clients. For
a new client, Innis has been authorized to invest up to 1.2 million in two investment funds:
a stock fund and a money market fund. Each unit of the stock fund costs E50 and provides
an annual rate of return of 10%; each unit of the money market fund costs E100 and
provides an annual rate of return of 4%. The client wants to minimize risk subject to the
requirement that the annual income from the investment be at least E60 000. According to
Innis’s risk measurement system, each unit invested in the stock fund has a risk index of 8,
and each unit invested in the money market fund has a risk index of 3; the higher risk index
associated with the stock fund simply indicates that it is the riskier investment. Innis’s client
also specified that at least E300,000 be invested in the money market fund. Letting:
x 1 ¼ units purchased in the stock fund
x 2 ¼ units purchased in the money market fund
leads to the following formulation:

Min 8x 1 þ 3x 2 Total risk
s:t:
50x 1 þ 100x 2 1; 200; 000 Funds available
5x 1 þ 4x 2 60; 000 Annual income
1x 2 3; 000 Minimum units in money market
x 1 ; x 2 0

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has
deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.