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Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section5.5: Shortest Path Models

Problem 32P

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Problem #2 - (E
- An Investment-Planning Problem
An investor has decided to invest a total of $50,000 among three investment opportunities: savings
certificates, municipal bonds, and stocks. The annual return on each investment is estimated to be 7%,
9% and 14%, respectively.
The investor does not intend to invest his annual interest returns (that is, he plans to use the interest to
finance his desire to travel). He would like to maximize his yearly return while investing a minimum of
$10,000 in bonds. Also, the investment in stocks should not exceed the combined total investment in
bonds and savings certificates.
And, finally, he should invest between $5,000 and $15,000 in savings certificates.
The problem is to determine the proper allocation of the resources ($50,000) among the three investment
opportunities. Thus, the decision variables are:
X1: dollars invested in savings certificates
X2: dollars invested in municipal bonds
X3: dollars invested in stocks
Formulate and explain the mathematical model for this LP problem, including:
a. The Objective Function
b. All the constraints that the solution must satisfy, including nonnegativity.

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