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 Bonds15% 3

Medium-term Bonds12%4

Government Bonds9%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.