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

VariableValueReduced CostS4000.000000.00000M10000.000000.00000ConstraintSlack/SurplusDual Value10.000000.0566720.000002.1666737000.000000.00000VariableObjective CoefficientAllowable IncreaseAllowable DecreaseS8.00000Infinite4.25000M3.000003.40000InfiniteConstraintRHS ValueAllowable IncreaseAllowable Decrease11200000.00000300000.00000420000.00000260000.0000042000.0000012000.0000033000.000007000.00000Infinite

(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 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_S

increases to 14 and

C_M

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.

Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. 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. 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. (a) Suppose the risk index for the stock fund (the value of CS ) 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 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 CS increases to 14 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