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Homework answers / question archive / One of its clients has just instructed the Heinlein and Krampt brokerage firm to invest $250,000 that she obtained recently through the sale of land holdings in Ohio
One of its clients has just instructed the Heinlein and Krampt brokerage firm to invest $250,000 that she obtained recently through the sale of land holdings in Ohio. The client has a good deal of trust in the firm, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm selects whatever stocks and bonds it believes are well rated, but within the following guidelines:
Municipal bonds, nursing home stock, and drug company stock should constitute at least 20%, 10%, and 10%, respectfully, of the total amount invested.
At least 40% of the funds should be placed in a combination of electronics and aerospace firms, with each accounting for 15%.No more than 50% of the total amount invested in electronics and aerospace firms should be placed in a combination of nursing home and drug company stock, both of which carry high risk.
Subject to these restraints, the client's goal is to maximize projected return on investments. The analysts at Heinlein and Kramft, aware of these guidelines, prepare a list of high-quality stocks and bonds and their corresponding rates of return:
Investment Projected Rate of Return
Los Angeles municipal bonds 5.3%
Thomas Electronics, Inc. 6.8%
United Aerospace Corp. 4.9%
Palmer Drugs 8.4%
Happy Days Nursing Homes 11.8%
I have used the Solver tool in Excel for this purpose. If you're not familiar with this tool, use the Help Center in Excel.
It was found that using a combination below, a maximized rate of return for the portfolio was found to be 7.21%.
Investment Projected Rate of Return Actual % invested
Los Angeles municipal bonds 5.30% 20%
Thomas Electronics, Inc. 6.80% 38%
United Aerospace Corp. 4.90% 15%
Palmer Drugs 8.40% 10%
Happy Days Nursing Homes 11.80% 17%
To help further, I suggest the formulation of the linear programming problem as below:
Let x1 and r1 stand for Los Angeles municipal bonds's investment fraction and its rate of return
Let x2 and r2 stand for Thomas Electronics, Inc.'s investment fraction and its rate of return
Let x3 and r3 stand for United Aerospace Corp.'s investment fraction and its rate of return
Let x4 and r4 stand for Palmer Drugs' investment fraction and its rate of return
Let x5 and r5 stand for Happy Days Nursing Homes' investment fraction and its rate of return
We formulate the problem as below:
Max
Subjected to
please see the attached file.
