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 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 what- ever stocks and bonds they believe are well rated but within the following guidelines:

● Municipal bonds should constitute at least 20% of the investment.

● At least 40% of the funds should be placed in a combination of electronic firms, aerospace firms, and drug manufacturers.

● 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 of return:

Investment	Projected Rate of Return (%)
Los Angeles municipal bonds	5.3
Thompson Electronics	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.

Answer 1

Let,

L be the dollar invested in Los Angels Municipal Bonds

T be the dollars invested in Thomson Electronics

U be the dollars invested in United Aerospace

P be the dollars invested in Palmer drugs

H be the dollars invested in Happy Days Nursing Homes

Z_max = 0.053L + 0.068T + 0.049U + 0.084P + 0.118H

Subject to;

Municipal Bonds

L>= 0.2(L+T+U+P+H)

= 0.8L – 0.2T – 0.2U – 0.2P – 0.2H

Combination of electronics, aerospace and drugs

T+U+P >= 0.4(L+T+U+P+H)

= -0.4L + 0.6T + 0.6U + 0.6P – 0.4H >=0

Nursing home as percent of bonds

H <=0.5L

H-0.5L =0

Funds to be invested

L+T+U+P+H <= 250000

Non negativity

L,T,U,P,H >=0

Placing values in exxcel and using excel solver;

Hence,

Total returns=$20,300

With the following investment strategy

$50,000 in Los Angeles Municipal Bonds

Zero investment in Thomson Electronics

Zero investment in United Aerospace

$175,000 investment in Palmer drugs

$25,000 investment in Happy Days Nursing Homes

NOTE: Please use excel solver and run the command, above table will help. Results are written below that