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

Essay

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 . They can also put their money in a vault (safe deposit vault), earning $0 \%$ and having a risk index of 0 . 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 to earn at least $\$ 80,000$ 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.