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 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 mamimize 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:

PROJECTED RATE

INVESTMENT OF RETURN $(\%)$

Los Angeles municipal bonds $5\mathrm{.}3$

Thompson Electronics, Inc. $6\mathrm{.}8$

United Aerospace Corp. $4\mathrm{.}9$

Palmer Drugs $8\mathrm{.}4$

Happy Days Nursing Homes $11\mathrm{.}8$

$($a$)$ Formulate this portfolio selection problem using

LP$.$

$($b$)$ Solve this problem.