Formulate a linear mathematical model

Assignment:

Q: A portfolio manager has developed a list of six investment alternatives for a multiyear horizon. These at Treasury bills, Common stock, Corporate bonds, Real estate, Growth funds, and Savings and loans. The investments and their various financial factors are described below. In the table, the return is given as at annual percentage, and the length represents the estimated number of years required for the annual retur to be realized. The risk coefficient is a subjective estimate representing the manager's appraisal of therelative safety of each alternative, on a scale of 1-10. The growth potential is an estimate of the potentia increase in value over the horizon.

 Portfolio Data Alternative TB CS CB RE GF SL Length (years) 4 7 8 6 10 5 Annual return (%) 6 15 12 24 18 9 Risk coefficient 1 5 4 8 6 3 Growth potential (%) 0 18 10 32 20 7

The manager wishes to maximize the return on a \$3 million portfolio, subject to the following restrictions:

1. The weighted average length should not exceed 7 years.

2. The weighted average risk coefficient should not exceed five.

3. The weighted average growth potential should be at least 10%.

4. The investment in real estate should be no more than twice the investment in stocks and bonds (i.e., in CS, CB, and GF) combined.

Formulate a linear mathematical model to achieve the manager's objective Clearly define your decision variables, objective and constraints