Funny Money Investments (FMI) has been authorized by one of its new clients to invest up to $1.2 million in two 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 new client wants to minimize the risk subject to the requirement that the annual income from the investment be at least $60,000. According to FMI’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. FMI’s new client wants at least $300,000 be invested in the money market fund. The following LP model is proposed, where S is the number of units purchased in the stock fund and M is number of units purchased in the money market fund:
Minimize 8 S + 3 M
Subject to 50 S + 100 M < 1,200,000
5 S + 4 M > 60,000
M > 3,000
S, M > 0
1. Solve the problem graphically using Algebra, and determine the optimal number of units to purchase of each type of fund and the corresponding rate of return for the portfolio. Explain the optimal solution and objective function value in the context of the problem.
2. Graphically and algebraically determine the sensitivity range of each objective function coefficient at the optimal solution of the linear program Explain the meaning of each range in the context of the problem.
3. Graphically and algebraically determine the sensitivity range of the right-hand-side value.
4. Calculate, using Algebra, the shadow price associated with each sensitivity range found
5. FMI is expecting the risk index of the stock fund to decrease to 6. What impact will this have on the current investment plan, the total risk of the portfolio and associated rate of return?
6. FMI is now expecting the risk index of the money market fund to increase to 7. What impact will this have on the current investment plan, the total risk of the portfolio and associated rate of return?