Mary Brown, an individual investor, has $70,000 to divide among several investments. The alternative investments are municipal bonds with an 8.5% annual return, certificates of deposit with a 5% return, treasury bills with a 6.5% return, and a growth stock fund with a 13% annual return. The investments are all evaluated after 1 year. However, each investment alternative has a different perceived risk to the investor; thus, it is advisable to diversify. Mary Brown wants to know how much to invest in each alternative in order to maximize the return.

The following guidelines have been established for diversifying the investments and lessening the risk perceived by the investor:

1. No more than 20% of the total investment should be in municipal bonds.

2. The amount invested in certificate of deposit should not exceed the amount invested in the

other three alternatives.

3. At least 30% of the investment should be in treasury bills and certificates of deposit.

4. To be safe, more should be invested in certificates of deposit and treasury bills than in

municipal bonds and growth stock funds, by a ratio of at least 1.2 to 1.

Mary Brown wants to invest the entire $70,000

REQUIRED:

1. Formulate a linear programming model for this problem.
2. Solve this model by using the computer.
3. State the optimal solution to the problem.
4. What constraints are non-binding?
5. Interpret the non-zero shadow prices in your output constraint table.
6. What would be the effect if the total amount invested decreased by $20,000?