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Linear Programming Problem - Maximization

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 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 z = 3U + 5H
Subject to:
25U + 50H ≤ 80,000 Funds available
0.50U + 0.25H ≤ 700 Risk maximum
1U ≤ 1000 U.S. Oil maximum
U, H ≥ 0
What is the optimal solution, and what is the value of the total annual return?

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