Question

Kathleen Allen has $100,000 to divide among several investments. The alternative investments are municipal bonds with a 5% return, certificate of deposits with a 5% return, treasury bills with a 6.5% return, and a growth stock with a 13% annual return. To minimize risk, Kathleen follows these guidelines:

1. No more than 20% of the total investment should be in municipal bonds.

2. The amount invested in certificates of deposit should not exceed the total amount invested in the other three alternatives.

3. At least 30% of the investments should be in treasury bills and certificate of deposits.

4. The amount invested in CDs and treasury bills should equal to or greater than the amount invested in municipal bonds and the growth stock fund.

Kathleen wants to know how much to invest in each alternative in order to maximize the return.

Answer 1

Let the amount invested in municipal bonds be Xm, Certificate of deposits be Xd, Treasury bills be Xt, growth stock be Xg

Based on the Annual returns rate given, total annual returns = 5%*Xm + 5%*Xd + 6.5%*Xt + 13%*Xg

We have to maximize this return, hence, we get Objective function as

Maximize Total returns R = 5%*Xm + 5%*Xd + 6.5%*Xt + 13%*Xg

Various constraints given can be written as follows:

Xm + Xd + Xt + Xg = 100,000...........Constraint for the amount available for investment

Xm <= 20%*(Xm + Xd + Xt + Xg).....Constraint for the maximum amount invested in municipal bonds

Xd <= (Xm + Xt + Xg)........................Constraint for the maximum amount in the certificate of deposits

Xt + Xd >= 30%*(Xm + Xd + Xt + Xg)..Constraint for minimum investment in treasury bills and certificate of deposits.

Xd + Xt >= Xm + Xg...........................Constraint for amount CDs, treasury bills to be greater than or equal to the amount invested in municipal bonds and the growth stock fund.

We solve the above problem in 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:

As seen from above solution:

Amount invested in municipal bonds = $0

Amount invested in certificate of deposits = $0

Amount invested in treasury bills = $50,000

Amount invested in growth stock = $50,000

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