$7-20$ A winner of the Texas Lotto has decided to invest

$$50,000$ per year in the stock market. Under con$-$

sideration are stocks for a petrochemical firm and a

public utility. Although a long$-$range goal is to get

the highest possible return, some consideration is

given to the risk involved with the stocks. A risk in$-$

dex on a scale of $1-10($with $10$ being the most risky$)$

is assigned to each of the two stocks. The total risk

of the portfolio is found by multiplying the risk of

each stock by the dollars invested in that stock.

The following table provides a summary of the

return and risk:

The investor would like to maximize the return on

the investment, but the average risk index of the in$-$

vestment should not be higher than $6.$ How much

should be invested in each stock? What is the aver$-$

age risk for this investment? What is the estimated