Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 7 - Section 7.6 - Linear Programming - Exercise Set - Page 872: 8

Answer

a. See graph b. $z(0,0)=(0)+6(0)=0$, $z(0,5)=(0)+6(5)=30$, $z(2,6)=(2)+6(6)=38$, $z(5,0)=(5)+6(0)=5$ c. maximum $z(2,6)= 38$, occurs at $(2,6)$.
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Work Step by Step

a. We can graph the system of inequalities representing the constraints as shown in the figure where the solution region is a four-sided area in the first quadrant. b. With the corner points indicated in the figure, we can find the values of the objective function as $z(0,0)=(0)+6(0)=0$, $z(0,5)=(0)+6(5)=30$, $z(2,6)=(2)+6(6)=38$, $z(5,0)=(5)+6(0)=5$, c. We can determine that the maximum value of the objective function is $z(2,6)= 38$, which occurs at $(2,6)$.
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