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: 6

Answer

a. see graph b. $z(0,0)=2(0)+3(0)=0$, $z(0,4)=2(0)+3(4)=12$, $z(3,2)=2(3)+3(2)=12$, $z(4,0)=2(4)+3(0)=8$ c. $12$, occurs on line segment from $(0,4)$ to $(3,2)$.
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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-side area in the first quadrant. b. With the corner points indicated in the figure, we can find the values of the objective function as $z(0,0)=2(0)+3(0)=0$, $z(0,4)=2(0)+3(4)=12$, $z(3,2)=2(3)+3(2)=12$, $z(4,0)=2(4)+3(0)=8$, c. We can determine the maximum value of the objective function as $12$, which occurs on line segment from $(0,4)$ to $(3,2)$.
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