Wiley Wiz is a mutual fund manager trying to decide how to divide up to $12 million between domestic and foreign stocks. Domestic stocks have been returning 11% per year and foreign 17%. Naturally, Wiley would like to maximize the annual return from his investments. Still, he wants to exercise some caution. No more that $10 million of the fund should go into domestic stocks and no more than $7 million into foreign. Also, at least half as much should be invested in foreign as domestic, and at least half as much in domestic as foreign to maintain some balance.

(a) Formulate a mathematical programming model with 5 main constraints to decide Wiley’s optimal investment plan using decision variables x1 ! millions of dollars invested in domestic stocks and x2 ! millions of dollars invested in foreign stocks.

(b) Enter and solve your model with the class optimization software.

(c) Using a 2-dimensional plot, solve your model graphically for an optimal investment plan.

(d) On a separate 2-dimensional plot, show graphically that the problem has alternative optimal solutions if rates of return are equal for domestic and foreign.