$2-32$ An investment broker has been given $$250,000$ to invest in a $12-$month commitment. The money can

be placed in Treasury notes $($with a return of $8\%$ and a risk score of $2)$ or in municipal bonds $($with a

return of $9\%$ and a risk score of $3).$ The broker's client wants diversification to the extent that

between $50\%$ and $70\%$ of the total investment must be placed in Treasury notes. Also, because of

fear of default, the client requests that the average risk score of the total investment should be no

more than $2\mathrm{.}42.$ How much should the broker invest in each security so as to maximize return on

investment?