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: 10

Answer

a. See graph b. $z(0,2)= -4$, $z(0,3)= -6$, $z(5,3)= 19$, $z(5,0)= 25$, $z(2,0)= 10$ c. maximum $ 25$ at $(5,0)$.
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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 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 $z(0,2)=5(0)-2(2)=-4$, $z(0,3)=5(0)-2(3)=-6$, $z(5,3)=5(5)-2(3)=19$, $z(5,0)=5(5)-2(0)=25$, $z(2,0)=5(2)-2(0)=10$, c. We can determine that the maximum value of the objective function is $z(5,0)=25$, which occurs at $(5,0)$.
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