Question

I need help with 10. a-f and 11. a-c

10. Recall the Innis Investments problem (Chapter 2, Problem 39). Letting S-units purchased in the stock fund M-units purchased in the money market fund leads to the following formulation: Min 8S+3M S0S+100OM1,200,000 Funds available S4M 60,000 Annual income 3,000 M Units in money market The computer solution is shown in Figure 3.16. a. What is the optimal solution, and what is the minimum total risk? h. Specify the objective coefficient ranges. c. How much annual income will be earned by the portfolio? d. What is the rate of return for the portfolio? e. What is the dual value for the funds available constraint? . What is the marginal rate of return on extra funds added to the portfolio? FIGURE 3.16 THE SOLUTION FOR THE INNIS INVESTMENTS PROBLEM Optinal objective Value 62000.00000 Variable Value Reduced Cost 000.00000 0.00000 0.00000 10000.00000 Constraint Slack/Surplus Dual Value 0.00000o 0.0000O 000.00000 0.05667 2.16667 Objective Allowable Allowable Variable Coefficient 8.00000 3.00000 Infinite 3.40000 4.25000o Infinite Allowable Allowable RHS Value Constraint 1200000.00000 60000.00000 3000.00000 300000.00000 42000.00000 7000.00000 420000.00000 12000.00000 Infinite 11. Refer to Problem 10 and the computer solution shown in Figure 3.16 a. Suppose the risk index for the stock fund (the value of C) increases from its current b. c. Suppose Cs increases to 12 and Cw increases to 3.5. How does the optimal solution value of 8 to 12 How does the optimal solution change, if at all? Suppose the risk index for the moncy market fund (the value of Cu) increases from its current value of 3 to 3.5. How does the optimal solution change, if at all? change, if at all?

Answer 1

a)Optimal Solution

S=4000

M=10000

Min. total risk=8S+3M=8*4000+3*10000=62000

b) Objective coefficient ranges

S ranges from (8-4.25) to infinity i.e 3.75 to infinity

M ranges from minus infinity to (3+3.4) i.e. minus infinity to 6.4

c) Annual income=8S+3M=8*4000+3*10000=62000