Consider the case of Welte Mutual Funds, Inc., located in New York City. Welte just

obtained $$100,000$ by converting industrial bonds to cash and is now looking for other

investment opportunities for these funds. Based on Welte's current investments, the firm's top financial analyst

recommends that all new investments be made in the oil industry, steel industry, or in government bonds.

Specifically, the analyst identified five investment opportunities and projected their annual rates of return. The

investments and rates of return are shown in the following Table.

INVESTMENT OPPORTUNITIES FOR WELTE MUTUAL F

Projected Rate of Retur

Investment

Atlantic Oil

Pacific Oil

Midwest Steel

Huber Steel

Government bonds

$(\%)$

$7\mathrm{.}3$

$10\mathrm{.}3$

$6\mathrm{.}4$

$7\mathrm{.}5$

$4\mathrm{.}5$

Management of Welte imposed the following investment guidelines.

Neither industry $($oil or steel$)$ should receive more than $$50,000.$

Government bonds should be at least $25\%$ of the steel industry investments.

The investment in Pacific Oil, the high$-$return but high$-$risk investment, cannot be

more than $60\%$ of the total oil industry investment.

What portfolio recommendations$-$investments and amounts$-$should be made for the

available $$100,000?$ Given the objective of maximizing projected return subject to the budgetary and

managerially imposed constraints, we can answer this question by formulating and solving a linear

programming model of the problem. The solution will provide investment recommendations for the

management of Welte Mutual Funds.