Question 3 - 16 Marks

Chrystab Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A 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 (0.50 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:

Max 8U + 5H Maximize total annual return

s.t.

25U + 50H 80,000 Funds available

0.50U+ .25H 700 Risk Maximum

1U 1000 U.S. Oli Maximum

U, H 0

The sensitivity report for this problem is shown in below in Table 1.

Table 1

Variable Cells
Model Variable	Name	Final Value	Reduced Cost	Objective Coefficient	Allowable Increase	Allowable Decrease
U	U.S Oil	800.000	0.000	3.000	7.000	0.5000
H	Huber	1200.000	0.000	5.000	1.000	3.5000
Constraints
Constraint Number	Name	Final Value	Shadow Price	Constraint R.H. Side	Allowable Increase	Allowable Decrease
1	Funds available	80000.000	0.093	80000.000	60000.000	15000.000
2	Risk maximum	700.000	1.333	700.000	75.000	300.000
3	U.S. Oil maximum	800.000	0.000	1000.000	1E+30	200.000

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 shadow prices for the constraints? Interpret each.

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