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 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 Innis' 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 of3. The higher risk index associated with the stock fund simply indicates that it is the riskier investment.Innis's client also specified that at least $300,000 be invested in the money market fund.Refer to the computer solution shown below.Optimal Objective Value = 62000.00000VariableSMConstraint123VariableSMConstraint1IN 32Value4000.0000010000.00000Reduced Cost0.000000.00000Slack/Surplus0.000000.000007000.000008.000003.00000Objective AllowableCoefficientIncreaseInfinite3.40000RHSValueDual Value-0.056672.166670.000001200000.0000060000.000003000.00000AllowableDecrease4.25000InfiniteAllowableIncrease300000.0000042000.000007000.00000AllowableDecrease420000.0000012000.00000Infinite (a) Suppose the risk index for the stock fund (the value of C) increases from its current value of 8 to 10. How does the optimal solution change, if at all?The optimal solution becomes (9600, 3000).The optimal solution does not change.(b) Suppose the risk index for the money market fund (the value of CM) increases from its current value of 3 to 4.5. How does the optimal solution change, if at all?The optimal solution becomes (9600, 3000).The optimal solution does not change.(c) Suppose C increases to 10 and CM increases to 4.5. How does the optimal solution change, if at all?The optimal solution becomes (9600, 3000).The optimal solution does not change.

The following computer solution (Sensitivity report) is provided for the question:

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 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 Innis' 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 specified that at least $300,000 be invested in the money market fund. Refer to the computer solution shown below. Optimal Objective Value - 62000.00000 Variable S M Constraint 1 2 3 Variable S M Constraint 1 2 3 Value Reduced Cost 0.00000 0.00000 4000.00000 10000.00000 Slack/Surplus 0.00000 0.00000 7000.00000 Objective Allowable Allowable Coefficient Increase Decrease Infinite 4.25000 3.40000 Infinite 8.00000 3.00000 RHS Value Dual Value -0.05667 2.16667 0.00000 1200000.00000 60000.00000 3000.00000 Allowable Increase Allowable Decrease 300000.00000 420000.00000 42000.00000 12000.00000 7000.00000 Infinite

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 34P