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 the 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 its portfolio risk index to be no more than 0.105 and wants to maximize the earnings of its portfolio. Formulate this as a linear program. Specify the decision variables, constraints, and the objective function.