Question

Linear Programming / Excel Solver

MJ Investments manages money for a variety of companies. It has three primary investments that it uses: The bonds return 4%, the traditional stock funds return 9%, and the growth stocks return 14%. The company always invests at least 20% of its portfolio in bonds. It also wants to invest at least twice as much in traditional stocks as it does in growth stocks. If the company has $2,000,000 to invest, how should it break down the investment in order to maximize return?

Answer 1

Let the amount invested in traditional stock be Xt, in growth stock be Xg, Bonds be Xb

Total Returns = 0.04*Xb + 0.09*Xt + 0.14*Xg

We have to maximize these returns

Subject to Constraints

Xb + Xt + Xg <= 2,000,000................Constraint for the amount available for investment

Xb >= 20% * (Xb + Xt + Xg)...............Constraint for a minimum amount in bonds

Xt >= 2*Xg..........................................Constraint for investing twice as much in traditional as a growth stock

Xb, Xt, Xg >= 0....................................Non-negativity constraint as the amount invested cannot be negative

We solve the above LPP in Excel using Excel Solver as shown below:

The above solution in the form of formulas along with Excel Solver extract is shown below for better understanding and reference:

The investment break-up is:

Bonds = 400,000

Traditional stocks = 1,066,666.67

Growth Stocks = 533,333.33

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