Investment Advisors Inc. Portfolio Optimization Homework Solution

This assignment analyzes an investment portfolio problem for Investment Advisors, Inc., focusing on maximizing annual returns. The portfolio consists of U.S. Oil and Huber Steel, with constraints on investment funds, risk, and the maximum shares of U.S. Oil. The linear programming formulation is provided, along with a sensitivity report. The optimal solution involves investing in 800 shares of U.S. Oil and 1200 shares of Huber Steel, resulting in a total annual return of $8400. The binding constraints are funds available and risk maximum. The shadow prices for funds available and risk maximum are $0.093 and $1.333 respectively. The U.S. Oil maximum constraint has a surplus of 200, indicating it is not binding. This analysis provides a comprehensive understanding of the optimal investment strategy and the impact of various constraints on portfolio performance.

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:
Ma
x 3U + 5H Maximize total annual
return
s.t.
25U + 50H ≤ 80,000 Funds available
0.50U + 0.25
H ≤ 700 Risk maximum
1U ≤ 1000 U.S. Oil maximum
U, H ≥ 0
The sensitivity report for this problem is shown in the figure below.
Optimal Objective Value = 8400.00000
Variable Value Reduced Cost
U 800.00000 0.00000
H 1200.00000 0.00000
Constraint Slack/Surplus Dual Value
1 0.00000 0.09333
2 0.00000 1.33333
3 200.00000 0.00000
Variable Objective
Coefficient
Allowable
Increase
Allowable
Decrease
U 3.00000 7.00000 0.50000
H 5.00000 1.00000 3.50000
Constraint RHS
Value
Allowable
Increase
Allowable
Decrease
1 80000.00000 60000.00000 15000.00000
2 700.00000 75.00000 300.00000
3 1000.00000 Infinite 200.00000
a. What is the optimal solution, and what is the value of the total annual return?
Optimal solution U
Optimal solution H
Estimated Annual Return $
b.
c. Which constraints are binding?
Constraint
Funds Avail. Binding
Risk Max Binding
U.S. Oil Max Non-Binding
d. What are the shadow prices for the constraints? If required, round your answers to three decimal places.
800
1200
8400

Constraint Shadow Price
Funds Avail.
Risk Max
U.S. Oil Max
0.093
1.333
0.000