Question: Portfolio Allocation

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 table below summarizes the annual return per share, price per share and risk index per share for the two stocks.

Managers are faced with the following constraints. They can invest up to $80,000 in the portfolio. The portfolio risk index must not exceed 700, and they are limited to a maximum of 1000 shares in U.S. Oil.

a. Formulate the LP model for this problem as a standard minimization or maximization problem.

b. Find the optimal solution of the problem using an LP software like Management Scientist.

c. Which constraint(s) are binding? Which constraints are non-binding?

d. Would it be beneficial to relax the constraint on purchases of U.S. Oil? Why or why not?