Question: With each paycheck, you invest up to $200 in your 401(k) retirement account. You would like to choose an optimal allocation between a stock fund and a bond fund to maximize your expect return, but you do not want the standard deviation of your total investment to exceed 15%. The stock fund has an expected return of 11% and standard deviation of 24% per dollar invested. The bond fund has an expected return of 5% and standard deviation of 4% per dollar invested. (Assume stock and bond returns are statistically independent.) The stock fund investments cannot be more than 75% of our total investment and the bond fund investments cannot be less than 10% of your total investment.

(a) Formulate the problem above as an LP to maximize expected return.

(b) Graph the feasible region of the LP.

(c) Solve the LP using the graphical method. What is your optimal allocation of your investments this paycheck? What is your expected return?