A trust officer at the Blacksburg National Bank needs to determine how to invest
ID: 437048 • Letter: A
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
==================================
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
==========================
At least 30% in tax-free investments
A + B + D 30,000
=============================
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)
========================
Nonnegativity conditions
A, B, C, D, E 0
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