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 1,000 shares of U.S. Oil. If the objective is to maximize total annual returns of the portfolio,
a. What is the optimal solution, and what is the value of the total annual return?
b. What is the optimal solution if the annual return for U.S. Oil changes from $3 to $8 per share (everything else stays the same)? What is the value of the total return?
c. What is the value of the optimal solution if the annual return of Huber Steel changes from $5 to $2 (everything else stays the same)? What is the value of the total return?