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	Value	Reduced Cost
S	4000.00000	0.00000
M	10000.00000	0.00000

Constraint	Slack/Surplus	Dual Value
1	0.00000	0.05667
2	0.00000	2.16667
3	7000.00000	0.00000

Variable	Objective Coefficient	Allowable Increase	Allowable Decrease
S	8.00000	Infinite	4.25000
M	3.00000	3.40000	Infinite

Constraint	RHS Value	Allowable Increase	Allowable Decrease
1	1200000.00000	300000.00000	420000.00000
2	60000.00000	42000.00000	12000.00000
3	3000.00000	7000.00000	Infinite

answer the following questions:

(a)Suppose the risk index for the stock fund (the value of

C_S) increases from its current value of 8 to 14. 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

C_M) increases from its current value of 3 to 5.5. How does the optimal solution change, if at all?

The optimal solution becomes (9600, 3000). The optimal solution does not change.

(c)Suppose C_S increases to 14 and C_M increases to 5.5. How does the optimal solution change, if at all?The optimal solution becomes (9600, 3000). The optimal solution does not change.