Midwest Money Manger (MMM), an investment firm, has $4 million to invest. They h
ID: 1941175 • Letter: M
Question
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)Explanation / Answer
Objective function is: Minimize: 0.2S + 0.11B + 0.07M + 0.01G
subject to following constraints
0.15S + 0.09B + 0.06M + 0.045G >=400000
S + B +M +G <= 4000000
S>=0
B>=0
M>=0
G>=0
Variables:
S - Stock
B- bbonds
M-money-market
G-government