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?
because
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?
because
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?
because two variables are not changing, the linear program to be
run again. The new solution
1) Suppose the risk index for the stock fund (the value of Cs) increases from its current value of 8 to 12. the optimal solution change is,
No change because the allowable increase is infinite. refer allowable increase of variable S in the sensitivity report
2) Suppose the risk index for the money market fund (the value of Cm) increases from its current value of 3 to 3.5. the optimal solution change is,
No change because the allowable increase is 3.40000. refer allowable increase of variable M in the sensitivity report
3. Suppose the value of Cs increases to 12 and the value of Cm increases to 3.5. the optimal solution change is,
No change because the two variables are not changing, the linear program does not need to be run again. The new solution remained the same. refer allowable increase of both variables S and M in the sensitivity report
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