Midwest Money Manger (MMM), an Investment Firm, Has $\$ 4$ Million to Invest

Midwest Money Manger (MMM), an investment firm, has $\$ 4$ million to invest. They have four choices, namely stocks, bonds, money-markets, and government securities. The respective projected yields are: $15 \%, 9 \%, 6 \%$ , and $4.5 \%$ . The respective risk indices are: $0.2,0.11,0.07$ , and 0.01 . It is assumed that the risk index of a portfolio is equal to the weighted average value of individual index, using the proportion of investment as weights. MMM wants to limit its investment in stocks and bonds to a maximum of $50 \%$ of the total investment. Investment in money markets should always be less than or equal to investment in government securities. MMM wants to earn at least $\$ 400,000$ in the next year and minimize the risk of its portfolio. Formulate this as a linear program. Specify the decision variables, constraints, and the objective function. Given the following formulation, verify the feasibility of the solution: Invest as follows: Stocks $=\$ 1,500,000$ ; Bonds $=\$ 750,000$ ; Money-market $=\$ 750,000$ ; Government securities $=\$ 1,000,000$ : is feasible. Is it feasible? Is it optimal?