The Heinlein and Krampf Brokerage firm has just been instructed by one of its cl

Question

The Heinlein and Krampf Brokerage firm has just been instructed by one of its clients to invest $250,000 of her money obtained recently through the sale of land holdings in Ohio. The client has a good deal of trust in the in¬vestment house, but she also has her own ideas about the distribution of the funds being invested. In par¬ticular, 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 max¬imize 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 of return.

Explanation / Answer

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

Let X1 = dollars invested in Los Angeles municipal bonds

      X2 = dollars invested in Thompson Electronics

      X3 = dollars invested in United Aerospace

      X4 = dollars invested in Palmer Drugs

      X5 = dollars invested in Happy Days Nursing Homes

Optimal Solution: X1 = $50,000   X2 = $0 X3 = $0   X4 = $175,000   X5 = $25,000   ROI = $20,300

Maximize .053X1 + .068X2 + .049X3 + .084X4 + .118X5 (maximize return on investment) Subject to: X1 + X2 + X3 + X4 + X5 250,000 (total funds available) .8X1 - .2X2 - .2X3 - .2X4 - .2X5 0 (municipal bond restriction) -.4X1 + .6X2 + .6X3 + .6X4 - .4X5 0 (electronics, aerospace, drugs combo) -.5X1 + X5 0 (nursing home as a percent of bonds) X1, X2, X3, X4, X5 0 (non-negativity constraints)

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