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 total annual return (before tax).   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 as 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.   Suppose the decision variable  represents the amount of money invested in bond  for . Formulate a linear programming (LP) model to solve the optimal strategy.   1. Write down the constraint using the defined decision variables requiring “invest as least 50% of the money in short-term issues”.   2. Write down the constraint using the defined decision variables requiring “at least 30% of the funds should go in tax-free investments”.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 50P
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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 total annual return (before tax).

 

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 as 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.

 

Suppose the decision variable  represents the amount of money invested in bond  for . Formulate a linear programming (LP) model to solve the optimal strategy.

 

1. Write down the constraint using the defined decision variables requiring “invest as least 50% of the money in short-term issues”.

 

2. Write down the constraint using the defined decision variables requiring “at least 30% of the funds should go in tax-free investments”.

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ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,