Question

Quantitative Models for Decision-Makers

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 $90 per share and the annual return for Huber Steel is $100 per share. U.S. Oil sells for $31 per share and Huber Steel sells for $42 per share. The portfolio has $60,000 to be invested. The portfolio risk index (0.50 per share of U.S. Oil and 0.50 per share for Huber Steel) has a maximum of 1,300. In addition, the portfolio is limited to a maximum of 20,000 shares of U.S. Oil.

Q: What is the optimal solution, and what is the value of the total annual return (rounded)?

• A. $150,200
• B. $174,200
• C. $8,700
• D. $5,600

Answer 1

B. $174,200

U = US Oil

H = Huber Steel

Maximize total annual returns function A, given by

A = 90U + 100H

Funds available 31U+42H ≤ 60000

Risk Maximum 0.5U+0.5H≤1300

Maximum shares of U.S. Oil 1U≤20000

U,H ≥0

Entering the following constraints in excel solver

Solving, we get

Hence, the total annual return (rounded) = 174200