Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each clients needs. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs $100 and provides an annual rate of return of 4%. The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $60,000. According to Inniss risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3; the higher risk index associated with the stock fund simply indicates that it is the riskier investment. Inniss client also specified that at least $300,000 be invested in the money market fund. Innis needs to determine how many units of each fund to purchase for the client to minimize the total risk index for the portfolio. Letting X1 = units purchased in the stock fund X2 = units purchased in the money market fund Leads to the following formulation: Min 8x1 + 3x2 Total risk s.t 50x1 + 100x2 1,200,000 Funds Available 5x1 + 4x2 60,000 Annual income 1x2 3,000 Minimum units in money market x1, x2 0 a.) Solve this problem using the simplex method. b.) The value of the optimal solution is a measure of the riskiness of the portfolio. What effect will increasing the annual income requirement have on the riskiness of the portfolio? c.) Find the range of feasibility for b2. d.) How will the optimal solution and its value change if the annual income requirement is increased from $60,000 to $65,000? e.) How will the optimal solution and its value change if the risk measure for the stock fund is increased from 8 to 9? a question