College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 5 - Systems of Equations and Inequalities - Exercise Set 5.6 - Page 580: 7

Answer

The objective function has maximum value 24 at (6,0)

Work Step by Step

The region that is defined by the constraints is * to the right of x=0 (the y=axis), * above the line y=0 (the x-axis), * below the line 2x+3y=12 (for this line, when x=0, y=4 and when y=0, x=6) * above the line x+y=3, (for this line, when x=0, y=3 and when y=0, x=3) The region is shaded red on the image below. The corners are (0,4), (0,3), (3,0) and (6,0). Calculating the objective function z=4x+y in each corner point, (table in step 6 of the image) we find that the objective function has maximum value 24 at (6,0)
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