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Please solve the following problems related to Introduction to Linear Programming (Chapter 7)
1. Mike Jackson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 5% for the bond fund and 8.5% for the stock fund.
Whatever portion of the inheritance Mike finally decides to commit to the trust fund, he wants to invest at least 30% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 7%.
Please answer the following questions.
a. Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives.
b. Solve the problem and find out the optimal solution.
2. ABC 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, ABC has been authorized to invest up to $1.3 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 7%, each unit of the money market fund costs $100 and provides an annual rate of the return of 4%.
The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $77, 000. According to ABC’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 5; the higher risk index associated with the stock fund simply indicated that it is the riskier investment. ABC’s client also specifies that at least $350,000 be invested in the money market fund.
Please answer the following questions.
a. Determine how many units of each fund ABC should purchase for the client to minimize the total risk index for the portfolio.
b. How much annual income will this investment strategy generate?
To compute optimal solution, you can use the method in the textbook or use the software (Excel Solver, Page 298-301 in the textbook)
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