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: 7

Answer

a. See graph b. $z(0,3)= 3$, $z(0,4)= 4$, $z(3,0)= 12$, $z(6,0)= 24$ c. maximum$ 24$, occurs at $(6,0)$.
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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 $z(0,3)=4(0)+(3)=3$, $z(0,4)=4(0)+(4)=4$, $z(3,0)=4(3)+(0)=12$, $z(6,0)=4(6)+(0)=24$, c. We can determine that the maximum value of the objective function is $z(6,0)= 24$, which occurs at $(6,0)$.
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