Problem: 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:
- Write down the decision variables.
- Write down the optimization statement for the objective function.
- Write down the constraints