Question

SESSION 9: 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 Annual 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. 1. Create the spreadsheet model and use Solver to solve the problem.

Answer 1

Creating the Linear Programming model to represent the problem: Decision variables are the amounts of money should be invested in each bond.

X₁ = Amount of money to invest in Bond A  

X₂ = Amount of money to invest in Bond B

X₃ = Amount of money to invest in Bond C

X₄ = Amount of money to invest in Bond D

X₅ = Amount of money to invest in Bond E

The objective is maximizing total annual return.

Maximize f(X₁, X₂, X₃, X₄, X₅) = 9.5%X₁ + 8%X₂ + 9%X₃ + 9%X₄ + 9%X₅

Constraints: Total investment: X₁ + X₂ + X₃ + X₄ + X₅ = 100,000.

X2 + X5 >= 50,000.

X1 + X4 + X5 <= 50,000.

X1 + X2 + X4 >= 30,000

9.5%X1 + 8%X2 + 9%X4 >= 40%(9.5%X1 + 8%X2 + 9%X3 + 9%X4 + 9%X5)

Nonnegativity constraints: X1, X2, X3, X4, X5 >= 0

Optimal solution:

Amount invested in Bond A = $20,339

Amount invested in Bond B = $20, 339

Amount invested in Bond C = $29, 661

Amount invested in Bond D = $0

Amount invested in Bond E = $29, 661

The Maximum annual return is $8,898