OPERATIONS RESEARCH >INTERNATIONAL EDITI
OPERATIONS RESEARCH >INTERNATIONAL EDITI
4th Edition
ISBN: 9780534423629
Author: WINSTON
Publisher: CENGAGE L
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Chapter 3.8, Problem 4P

Explanation of Solution

 Formulation of a Linear Programming (LP) to maximize total profit earned from Erica’s investment:

 Let “x1” be the number of dollars invested in stocks.

 The “x2” be the number of dollars invested in loans.

 As every dollar invested in stocks gives 10 cents profits, so the total profit on stocks would be $0.1x1. Likewise, the total profit on loan would be $0.15x2.

 Since the objective is to maximize total profit earned from Erica’s investment, the objective function is defined as follows:

 Max Z=0.10x1+0.15x2

 Constraint 1:

 At least, 30% of total invested money must be invested in stocks. The “x1+ x2” is the total money invested in the investment. Since the number of dollars invested in stocks must be at least 30% of the total investment, the constraint is defined as follows:

 x10.3(x1+x2)0.7x10.3x20

 Constraint 2:

 At least, $400 of all money must be invested in loans, so the constraint is defined as:

 x2400

 Constraint 3:

 At most, $1000 is invested in stocks and loans, so the constraint is defined as:

 x1+x21000

 Therefore, the formulation to the given linear program is:

 Max Z=0

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Chapter 3 Solutions

OPERATIONS RESEARCH >INTERNATIONAL EDITI

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