linear programming

Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each clientâ??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 Innisâ??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. Innisâ??s client has also specified 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 z = 8S + 3M

Subject to:

50S + 100M â?¤ 1,200,000 Funds available

5S + 4M > 60,000 Annual income

M â?¥ 3,000 Units in money market

S, M â?¥ 0

a. Determine how many units of each fund Innis should purchase for the client to minimize the total risk index for the portfolio.

b. How much annual income will this investment strategy generate.

c. Suppose the client desires to maximize annual return, How should the funds be invested.

***please show all work and output of any programming used*****