Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's 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 funds costs $50 and provides an annual rate of return of 10%; each unit of the money market funds 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 Innis's 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. Innis's client also specifies that at least $300,000 be invested in the money market fund.

Assuming that the company wants to minimize the total risk index for the portfolio (Let S=number of units purchased in the stock funds, M=number of units purchased in the money market fund), answer the following questions:

1)What is the linear programming model for this problem?

2)Find the optimal solution (the minimum total risk) and the sensitivity report using Excel's solver.

3)How much annual income will this investment strategy will generate?

4)Suppose the client desires to maximize annual return. How should the funds be invested?

5)Specify the objective coefficient ranges.

6)What is the rate of return for the portfolio?

7)What is the shadow price for the funds available constraint?

8)Suppose the risk index for the stock fund (the objective function coefficient for S) increases from its current value of 8 to 12. How does the optimal solution change, if at all?

9)Suppose the risk index for the money market fund (the objective function coefficient for M) increases from its current value of 3 to 3.5. How does the optimal solution change, if at all?

10)Suppose the objective function coefficient for S increases to 12 and the objective function coefficient for M increases to 3.5. Can you determine how the optimal solution will change using the Sensitivity Analysis report?

Microsoft Excel 16.0 Sensitivity Report Worksheet: [HW8.xlsx]Sheet1 Report Created: 7/16/2019 12:12:59 PM Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$14 Units Produced Stocks 4000 0 8 1E+30 4.25 $C$14 Units Produced Mon Mkt 10000 O 3 3.4 1E+30 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $B$19 Unit Cost Amt. Used 1200000 -0.056666667 1200000 300000 420000 $B$20 Annual Return Amt. Used 60000 2.166666667 60000 42000 12000 $B$21 Min. Money Market Amt. Used 10000 0 3000 7000 1E+30