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Linear Programming Modeling for Investment Optimization

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A Brokerage firm has just been instructed by one of its clients to invest $250,000 for her money obtained recently througn 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: a) Municipal bonds should constitute at least 20% of the investment. b) At least 40% of the funds should be placed in a combination of electronic firms, aerospace firms, and drug manufacturers. c) 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 the brokerage firm, aware of these guideline, prepare a list of high-quality stocks and bonds and their corresponding rates of return:

Investment Protected 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 Home 11.8

a) Formulate this portfolio selection problem using LP.
b) Solve this problem.

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Please see the attachment.

a) Formulate this portfolio selection problem using LP.

The LP model is ...

Solution Summary

Attachments include the LP model is attached in a PDF. The Solution is done in Excel with Solver and attached.

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(a) Suppose that at most two of the project 1 - 5 can be selected. write the appropriate algebraic constraint and solve. What is the new Z*?
(b) Suppose that if investment 1 is selected, then investment 3 must also be selected. Write the appropriate algebraic constraint and solve. What is the new Z*?
(c) Suppose that at least one of the investments 6 and 7 must be selected. Write the appropriate algebraic constraint and solve. What is the new Z*?
(d) Suppose that investment 2 can be selected only if both investments 1 and 3 are selected. Write the appropriate algebraic constraint and solve. What is the new Z*?

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