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’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.
Letting
S = units purchased in the stock fund
M = units purchased in the money market fund

leads to the following formulation:
Min 8S + 3M
s. t.
50S + 100M ≤ 1,200,000 Funds available
5S + 4M ≥ 60,000 Annual income
M ≥ 3,000 Units in money market
S, M ≥ 0

The sensitivity report is shown in the figure 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

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

(Options are: change, no change or unkown)because (options are: the allowable increase is 3, the allowable increase is 4.25, the allowable increase is 30,000, the allowable increase is infinite).
Suppose the risk index for the money market fund (the value of Cm) increases from its current value of 3 to 3.5. How does the optimal solution change, if at all?

(options are: no change, change, or unknown) because (options are: the allowable increase is 3, the allowable increase is 4.25, the allowable increase is 30,000, the allowable increase is infinite).
Suppose the value of Cs increases to 12 and the value of Cm increases to 3.5. How does the optimal solution change, if at all?

(options are: no change, change, or unknown) because two variables are not changing, the linear program (options are: needs, does not need) to be run again. The new solution (options are, remained the same or has changed).