Philip Jones just inherited $1,000,000 from his uncle. There was a stipulation in the will that Philip invests the million dollars for five years before Philip can have complete access to the capital, although he can spend any interest. Philip went to an investment counselor, who suggested that Philip invest with two types of mutual funds. The first mutual fund—the Alpha Fund—focuses on growth stocks and has an anticipated return of 10% a year. The second mutual fund—the Beta Fund—is composed mostly of Blue Chip stocks and has an estimated annual return of 6%. The Alpha Fund being a high-growth fund is riskier, with a risk coefficient of 1.5. The Beta Fund is actually less risky than the market at large and has a risk coefficient of 0.8. Philip took a test given by the investment counselor, and it was determined that the maximum risk coefficient for him would be 1.2. The cost of one unit of the Alpha Fund is $10,000 while a unit of the Beta Fund costs $5,000. Philip wants an interest income of $65,000 a year for the years that the money is invested.

1. a. What would be the decision variables and the objective function for Philip if he wished to maximize his interest income?

The Decision Variables – Decision Variable 1 – Alpha Fund / Decision Variable 2 – Beta Fund

The Objective Function – To maximize the total return. (.1d1+.06d2)

2. Write down all the constraints.

Constraints –

Coefficient Risk	$1200000	<=	$1200000
Yearly interest	$82,857.14	>=	$65,000
Total investment	$ 1,000,000.00	<=	$1,000,000
d1	571428.6	>=	0	Nonnegative
d2	428571.4	>=	0	Nonnegative

3. b. What would be the optimal solution (i.e., values of decision variables) and optimal value (i.e., the value of the objective function? Round your answers to the nearest integer.

Optimal Solution

570000 / 10000 = 570

Optimal Value

430000 / 5000 = 86

4. c. Philip questions the test that determined that his maximum risk coefficient would be 1.2. He feels that it should be 1.0, which is the same as the average market. What are the new optimal solution and optimal values?

Optimal Solution

Optimal Value