Business Question:

Consider Welte Mutual Funds, Inc., located in New York City. Welte just obtained $$100,000$ and is looking for investment opportunities for these funds. Based on Welte$$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.

Table: Rate of Returns

Assignment $3$: Welte Mutual Funds via Linear Programming

$$Investment$$Projected Rate of Return $(\%)$Atlantic Oil$7\mathrm{.}3$Pacific Oil$10\mathrm{.}3$Midwest Steel$6\mathrm{.}4$Huber Steel$7\mathrm{.}5$Government bonds$4\mathrm{.}5$Management of Welte imposed the following guidelines:

$1)$ Neither industry $($oil or steel$)$ should receive more than $$50,000.$

$2)$ Government bonds should be at least $25\%$ of the steel industry

investments.

$3)$ The investment in Pacific Oil, the high return but high$-$risk investment,

cannot be more than $60\%$ of the total oil industry investment.

Objective:

What portfolio recommendations$$investments and amounts$$should be made for the available $$100,000?$