Mr. Jones has dollar 12,000 to invest in three types of stocks, low risk, medium

Question

Mr. Jones has dollar 12,000 to invest in three types of stocks, low risk, medium risk, and high -risk He Invests three principles The amount invested in low risk stocks will be at most dollar 2,000 more than the amount Invested to medium risk stocks At least 54 .000 will be invested m low and medium risk stocks No more than dollar 10, 000 wife invested in medium- and high risk stocks The expected yields are 6% tor low- risk stocks. 7% tor medium -risk and 8% for high-risk stocks How much money should Mr Jones invest in each type of stock to maximize Ms total expected yield? Mr Jones should invest S in low-ash stocks, S in medium risk stocks and in high-risk stocks

Explanation / Answer

according to problem we will have to suppose like that

Let L, M, H denote the amount of Low, Medium, and High risk stocks.

We nose the total amount is 12,000, so the first equation is

L + M + H = 12000

The amount in low risk stocks will be at most 2000 more than medium

L - M < 2000

At least 4000 will be invested in medium and high risk

M + H > 4000

No more than 10000 will be invested in M and H stocks

M + H < 10000

The expected yields are 6% for low risk stocks, 7% for medium risk stocks, and 8% for high risk stocks.

maximize profit as:

.06L + .07M + .08H = profit

by using graph we will have

L = 4000

M = 2000

H = 6000

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