Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for

Question

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 (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:

Explanation / Answer

a). Variable U, H Values is given in the sensitivity report (first table)

Optimal Solution U = 800

Optimal Solution H = 1200

Estimated Annual Return = 8400

b). Referring to Sensivity report (2nd table)

Those variables whose slack is zero are binding constraints. So constraints Funds Available and Risk Maximum are binding constraints.

c). Shadow prices (Dual Values) are given in the second table

Shadow price of constraint Funds Available = 0.093

Shadow price of constraint Risk Maximum = 1.333

Shadow price of US oil maximum = 0

Interpretation of shwdow price

fill in the blanks objective value

0.0933 and increase by 0.0933

1.333 and increase by 1.3333

0 and remain same

constraint is binding

US oil U/S

d). No, it is non-binding constraint.

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