1. The U-save company is planning its operations for the next year. The company is considering investing in four types of securities. The company has $1 million available for investment. The expected annual return and the risk index of each security are as follows:

Expected return Risk index

(%)

Long-term Bonds 15% 3

Medium-term Bonds 12% 4

Government Bonds 9% 7

Short-term Bonds 10% 9

The company wants to maximize the expected return from its bond investments, subject to the following restrictions:

• The average risk index of the portfolio should not exceed 6
• At most 45% of the total amount (1 million) can be invested in any single bond
• The expected return of the Government bond portfolio should be at least 1.2 times the return of the Long term and medium term bond portfolio.

Formulate the problem as a LP problem. Define the decision variables carefully. Use any software at your disposal to obtain an optimal solution.