[Solved] Intel Investments, Inc. manages funds for a number of companies and wealthy clients
Intel Investments, Inc. manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client’s needs. For a new client, Intel has been authorized to invest up to $1.5 million in two investment funds: a high-risk stock fund and a low-risk money market fund. Each unit of the stock fund costs $200 and provides an annual rate of return of 20%; each unit of the money market fund costs $300 and provides an annual rate of return of 3%. The client is content with minimizing risk subject to the requirement that the annual income from the investment be at least $200,000. According to Intel’s risk measurement system, each unit invested in the stock fund has a risk index of 10, and each unit invested in the money market fund has a risk index of 6. Intel’s client also specified that at least $500,000 has to 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 10S + 6M
s.t.
200S + 300M ≤ 1,500,000 Funds available
0.15*200S + 0.03*300M ≥ 200,000 Annual Income
M ≥ 500,000/300 Units in money market
S, M ≥ 0
The computer solution is shown below:
| Cell | Name | Final Value | Reduced | Objective | Allowable | Allowable |
| Cost | Coefficient | Increase | Decrease | |||
| $B$15 | Units Invested S | 4625 | 0 | 10 | 16.6666667 | 10 |
| $C$15 | Jars Produced F | 1666.666667 | 0 | 6 | 1E + 30 | 3.75 |
| Cell | Name | Final Value | Shadow | Constraint | Allowable | Allowable |
| Price | R.H. Side | Increase | Decrease | |||
| $B$20 | Whole tomatoes LHS | 1425000 | 0 | 150000 | 1E + 30 | 75000 |
| $B$21 | Tomato Sauce LHS | 200000 | 0.25 | 200000 | 15000 | 1942.857143 |
| $B$22 | Onion & Jalapeno LHS | 1666.666667 | 3.75 | 1666.66667 | 294.117647 | 1666.666667 |
Suppose the risk index for the stock fund (the value of S) increases from its current value of 10 to 12. How does the optimal solution change, if at all?
- Suppose the risk index for the money market fund (the value of M) increases from its current value of 6 to 8. How does the optimal solution change, if at all?
- Suppose S increases to 12 and M increases to 8. How does the optimal solution change, if at all?
Expert Answer
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