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THE TAIWAN ELECTRONIC COMMUNICATIONS (TEC) PROBLEM 125

7 Refer again to Problem 3.
a. Suppose the objective function coefficient of x 1 is increased to 3 and the objective
function coefficient of x 2 is increased to 4. Find the new optimal solution.
b. Suppose the objective function coefficient of x 1 is increased to 3 and the objective
function coefficient of x 2 is decreased to 2. Find the new optimal solution.

8 Recall the GulfGolf glove problem (Chapter 2, Problem 13). Letting:
R ¼ number of regular gloves

P ¼ number of professional gloves
leads to the following formulation:

Max 5R þ 8P
s:t
3
R þ / 2 P 900 Cutting and dyeing
1
1 / 2 R þ / 3 P 300 Finishing
1 1
/ 8 R þ / 4 P 100 packaging and shipping
R; P 0

The computer solution obtained using The Management Scientist is shown in Figure
3.15.
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 prices for the resources? Interpret each.
d. If overtime can be scheduled in one of the departments, where would you recommend
doing so?
9 Refer to the computer solution in Figure 3.15 (see Problem 8).
a. Calculate the ranges of optimality for the objective function coefficients.
b. Interpret the ranges in part (a).
c. Interpret the range of feasibility for the right-hand sides.
d. How much will the value of the optimal solution improve if 20 extra hours of packaging
and shipping time are made available?

10 Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a
number of clients. A particular portfolio consists of U shares of United Oil and H shares of Huber
Steel. The annual return for United Oil is E3 per share and the annual return for Huber Steel is E5
per share. United Oil sells for E25 per share and Huber Steel sells for E50 per share. The portfolio
has E80000 to be invested. The portfolio risk index (0.50 per share of United Oil and 0.25 per
share of Huber Steel) has a maximum of 700. In addition, the portfolio is limited to a maximum of
1000 shares of United Oil. The linear programming formation that will maximize the total annual
return of the portfolio is as follows:

Max 3U þ 5H Maximize total annual return
s:t
25U þ 50H 80; 000 Funds available
0:50U þ 0:25H 700 Risk maximum
1U 1000 United Oil maximum
U; H 0

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