Question

LP Model - St. Louis Investment Company Case St. Louis Investment Company possesses a large amount of cash, say $1,000,000. There are five different investment choices with different growth and income potentialities: common stocks, mutual funds, municipal bonds, savings certificates, and real estate investments. The current returns from the investment of each of these five choices are also different. The current returns on investment are known for each of the investment as follows: Common Stocks Mutual Funds Municipal Bonds Savings Certificates Real Estate Investment 10% per year 8% per year 6% per year 5% per year 9% per year Management believes the current yield will persist in the future and wishes to diversify the investment portfolio of the company to obtain the investment in common stocks to not more than the combined total investment in municipal bonds, savings certificates, and real estate investment. Total investment in mutual funds and real estate combined must be at least as large as that in municipal bonds. Also, management wishes to restrict its investment in mutual funds to a level not exceeding to that in savings certificates. Determine the optimum allocation of investment funds among these five choices and the actual amount of returns form investment under the above conditions. • Define the decision variables: X1 = X3 = X4= X5 = • Formulate the objective function: • Formulate the constraints: | Develop a spreadsheet application using MS-Excel Solver Add-in.

Answer 1

Decision Variables are as follows: Let investment in different options be

X1 = Common Stock

X2 = Mutual Funds

X3 = Municipal Bonds

X4 = Savings Certificates

X5 = Real Estate Investments

Objective Function:

Maximize Z = (0.1*X1) + (0.08*X2) + (0.06*X3) + (0.05*X4) + (0.09*X5)

Formulation of Constraints

• X1  $\leq$ (X3 + X4 + X5)
• (X2 + X5) $\geq$ X3
• X2 $\geq$ X4
• X1, X2, X3, X4, X5 $\geq$ 0
• X1 + X2 + X3 + X4 + X5 $\leq$ $1,000,000