A trust officer at the Blacksburg National Bank needs to determine how to invest

Question

A trust officer at the Blacksburg National Bank needs to determine how to invest $100,000 in the following collection of bonds to maximize the annual return.

Bond Return Maturity Risk
Tax-Free

A 9.5% Long High Yes
B 8.0% Short Low Yes
C 9.0% Long Low No
D 9.0% Long High Yes
E 9.0% Short High No
The officer wants to invest at least 50% of the money in short-term issues and no more than 50% in high-risk issues. At least 30% of the funds should go in tax-free investments, and at least 40% of the total annual return should be tax free.

Formulate an LP model for this problem in a spreadsheet and solve with Solver.

How much money should be invested in each Bond?

Explanation / Answer

MAX:

0.095A + 0.08B + 0.09C + 0.09D + 0.09E

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Total amount is invested

A + B + C + D + E = 100,000

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At least 50% in short-term issues

B + E 50,000

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No more than 50 % in high-risk issues

A + D + E 50,000

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At least 30% in tax-free investments

A + B + D 30,000

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At least 40% of the total annual return be tax-free

0.095A + 0.08B + 0.09D 0.4* (0.095A + 0.08B + 0.09C + 0.09D+ 0.09E)

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Nonnegativity conditions

A, B, C, D, E 0

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