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: 9

Answer

a. See graph b. $z(1,2)= -1$, $z(1,4) =-5$, $z(5,8)= -1$, $z(5,2)= 11$, c. maximum $z(5,2)= 11$, occurs at $(5,2)$.
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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-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 $z(1,2)=3(1)-2(2)=-1$, $z(1,4)=3(1)-2(4)=-5$, $z(5,8)=3(5)-2(8)=-1$, $z(5,2)=3(5)-2(2)=11$, c. We can determine that the maximum value of the objective function is $z(5,2)= 11$, which occurs at $(5,2)$.
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