Question: 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 number of shares to buy for each stock, so as to maximize the total estimated return.
Answer the following questions:
1) Write down the decision variables.
2) Write down the optimization statement for the objective function.
3) Write down the constraints