Set up this decision problem as an LP model in general form.
You have been given $100,000 by a client to invest in the stock market. After some preliminary analysis, you find that there are five stocks that you want to consider for your client's investment portfolio. The price per share, expected annual rate of return, and risk index for each of the five stocks are summarized in the table below:
|
Stock
|
Price per Share ($)
|
Expected Annual Return ($)
|
Risk Index per Share ($)
|
|
Monsanto
|
85
|
15
|
0.15
|
|
Dean Foods
|
20
|
5
|
0.06
|
|
Kraft Foods
|
23
|
8
|
0.09
|
|
General Mills
|
52
|
10
|
0.12
|
|
Whole Foods
|
20
|
6
|
0.05
|
The risk index for each stock is your client's opinion of the riskiness of each invest- ment. Your client has put a limit of 200 as the total amount of risk she will bear for the entire portfolio (total risk = risk index per share X number of shares). In addition, she does not want to invest in more than 500 shares of Monsanto stock. Finally, you cannot invest more than the $100,000 that your client has given to you. Your objective is to maximize the expected annual return for your client's portfolio. Assume that your commission does not figure into this exercise.