This is your lucky day. You have won a $20,000 prize. You aresetting aside $8,000 for taxes and partying expenses, but you havedecided to invest the other $12,000. Upon hearing the news, twodifferent friends have offered you an opportunity to become apartner in two different entrepreneurial ventures, one planned byeach friend. In both cases, this investment would involve spendingsome of your time next summer as well as putting up cash. Becominga full partner in the first friend’s venture would require aninvestment of $10,000 and 400 hours, and your estimated profit(ignoring the value of your time) would be $9,000. Thecorresponding figures for the second friend’s venture are $8,000and 500 hours, with an estimated profit to you of $9,000. However,both friends are flexible and would allow you to come in at anyfraction of a full partnership you would like. If you choose afraction of a full partnership, all the above figures given for afull partnership (money investment, time investment, and yourprofit) would be multiplied by this fraction. Because you werelooking for an interesting summer job anyway (maximum 600 hours),you have decided to participate in one or both friends’ ventures inwhichever combination that would maximize your total estimatedprofit. You need to solve the problem of finding the bestcombination.

a) Use the graphical solution method to solve this problem.Clearly display the feasible region of the problem and its optimalsolution.

b) What profit would the first friend have to offer you in orderto be optimal to invest your money and time to become his fullpartner?