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: 12

Answer

a. See graph b. $z(0,3)= 12$, $z(0,9)= 36$, $z(9,0)= 18$, $z(6,0)= 12$, $z(1.5,1.5)= 9$ c. maximum $ 36$ at $(0,9)$.
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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 pentagon shaped area in the first quadrant. b. With the corner points indicated in the figure, we can find the values of the objective function as $z(0,3)=2(0)+4(3)=12$, $z(0,9)=2(0)+4(9)=36$, $z(9,0)=2(9)+4(0)=18$, $z(6,0)=2(6)+4(0)=12$, $z(1.5,1.5)=2(1.5)+4(1.5)=9$, c. We can determine that the maximum value of the objective function is $z(0,9)=36$, which occurs at $(0,9)$.
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