The Heinlein and Krampf Brokerage firm has just been instructed by one of its clients to invest $250,000 for her, money obtained recently through the sale of land holdings in Ohio. The client has a good deal of trust in the investment house, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select whatever stocks and bonds they believe are well rated, but within the following guidelines:
1. Municipal bonds should constitute at least 20% of the investment.
2. At least 40% of the funds should be placed in a combination of electronics firms, aerospace firms, and drug manufacturers.

3. No more than 50% of the amount invested in municipal bonds should be placed in a high-risk, high-yield nursing home stock.

Subject to these restraints, the client’s goal is to maximize projected return on investments. The analysts at Heinlein and Krampf, aware of these guidelines, prepare a list of high-quality stocks and bonds and their corresponding rates and return.

Investment Projected rate of Return (%)
Los Angeles municipal bonds 5.3
Thompson Electronics, Inc. 6.8
United Aerospace Corp. 4.9
Palmer Drugs 8.4
Happy Days Nursing Homes municipal bonds 11.8

a. Formulate this portfolio selection problem using LP.

b. Solve the problem using Excel. 
c. What is the optimal projected return? How much to invest in each investment type? 

d. How much money has been invested in Electronics and Aerospace?

e. What are the binding constraints? 

f. If you have the chance to relax one of the guideline restrictions, which one do you choose and why?

g. If the projected rate of return of the municipal bonds increases to 6.1, what will happen to the investment solution found in b? Is it require to resolve the problem using Excel or we are able to derive the solution? Find the solution.