1. Kathleen Allen, an individual investor, has $100,000 to divide among several investments.The alternative investments are municipal bonds (MB) with an 8.5% annual return and a risk index of 6; certificates of deposit (CD) with a 5% return and a risk index of 2; treasury bills (TB) with a 6.5% return and a risk index of 4; and a growth stock fund (GS) with a 13% annual return and a risk index of 8.The investments are all evaluated after one year.However, each investment alternative has a different perceived risk to the investor given by the risk index; thus, it is advisable to diversify.Kathleen wants to know how much to invest in each alternative in order to maximize the total dollar return in one year's time.

The following guidelines have been established for diversifying the investments and controlling the overall risk perceived by the investor.

a.The entire $100,000 fund must be allocated to the four investment classes;

b.The weighted average risk index for the portfolio will be no more than 5;

c.The amount invested in each alternative shall be at least 12% of the total investment;

d.No more than 20% of the total investment should be in municipal bonds;

e.The amount invested in certificates of deposit should not exceed the average of the amounts invested in the other three alternatives;

f.At least 30% of the investment should be in treasury bills and certificates of deposit;

g.More should be invested in CDs and treasury bills than in municipal bonds and the growth stock fund by a ratio of at least 1.2 to 1.

Formulate Kathleen's portfolio optimization problem as a linear programming problem.Include your definition of variables, the objective function, and the list of constraints.