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: 5

Answer

a. See graph b. $z(0,4)= 8$, $z(0,8)= 16$, $z(4,0)= 12$, c. Maximum $ 16$, at $(0,8)$.
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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 triangle in the first quadrant. b. With the corner points indicated in the figure, we can find the values of the objective function as $z(0,4)=3(0)+2(4)=8$, $z(0,8)=3(0)+2(8)=16$, $z(4,0)=3(4)+2(0)=12$, c. We can determine the maximum value of the objective function as $z(0,8)= 16$, which occurs at $(0,8)$.
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