Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A particular portfolio consists of shares of U.S. Oil and 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. Ol and 0.25 per share for Huber Steel) has a maximum of 700. In addition, the portfolio is limted to a maximum of 1000 shares of U.S. Oil. The liner programming formulation that will maximize the total annual return of the portfolio is as follows: Max                    3U + 5H                                                                                       Maximize total annual return s.t. 25U +  50H less than or equal to 80,000                                        Funds available 0.50U  +   0.25D less than or equal to 700                                     Risk maximum 1U less than or equal to 1000                                                         U.S. Oil maximum U, H greater than or equal to 0 Grading Rubric is as follow: Purchase the answer to view it

The linear programming problem given in the question aims to maximize the total annual return of a portfolio consisting of shares of U.S. Oil and Huber Steel. The problem is subject to certain constraints, such as the funds available for investment, the maximum risk index, and the maximum number of shares of U.S. Oil.

The objective function is to maximize the total annual return (denoted by R) of the portfolio. It is represented as:

Maximize R = 3U + 5H

Where U denotes the number of shares of U.S. Oil in the portfolio and H denotes the number of shares of Huber Steel in the portfolio.

The problem is subject to the following constraints:

1. Funds available constraint: The total cost of U.S. Oil shares and Huber Steel shares should not exceed the funds available for investment in the portfolio. This is given by the inequality:

25U + 50H ≤ 80,000

Where 25 denotes the cost per share of U.S. Oil and 50 denotes the cost per share of Huber Steel.

2. Risk maximum constraint: The risk index of the portfolio, calculated by multiplying the risk of U.S. Oil per share (0.50) with the number of U.S. Oil shares (U) and adding it to the risk of Huber Steel per share (0.25) multiplied by the number of Huber Steel shares (H), should not exceed the maximum risk index of 700. This is represented as:

0.50U + 0.25H ≤ 700

3. U.S. Oil maximum constraint: The number of shares of U.S. Oil (U) should not exceed the maximum limit of 1000 shares. This is given by the inequality:

U ≤ 1000

Lastly, non-negativity constraints are imposed. U and H should be greater than or equal to zero.

The goal is to find the values of U and H that maximize the total annual return of the portfolio while satisfying the constraints. The linear programming problem can be solved using various optimization techniques, such as the simplex method or the graphical method.

By solving the linear programming problem, one can find the optimal number of shares of U.S. Oil and Huber Steel to invest in to maximize the total annual return of the portfolio, given the constraints on funds, risk, and the maximum number of shares of U.S. Oil.