A client asks his stockbroker to invest $100,000 for maximum annual income, subject to the three conditions: 1. Spread the investment over no more than three different stocks. 2. Put no more than 40 percent of the money into any one stock 3. Put a minimum of $10,000 into an oil stock.

A client asks his stockbroker to invest $100,000 for maximum annual income, subject to the three conditions:
1. Spread the investment over no more than three different stocks.
2. Put no more than 40 percent of the money into any one stock
3. Put a minimum of $10,000 into an oil stock.

The broker has identified three stocks for investment. Their estimated annual returns per share and price per share are shown in the following table:

Stock. Price per share. Estimate Annual Return per Share
Oil. $120. $11
Auto. $52. $4
Pharmaceutical. $18 $2

The client wishes to use LP to determine the optimal investment portfolio (number of shares to buy for each stock) so as to maximize the total estimated return.

Answer the following questions:
2.1) Write down the decision variables.

2.2) Write down the optimization statement for the objective function.

2.3) Write down the constraints.

2.4) With the aid of Excel Solver, what is the optimal portfolio? (Please hand in a printed copy of the report)

2.5) By Excel Solver, what is the sensitivity report?