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: 14

Answer

a. See graph b. $z(0,10)= 60$, $z(10,0)= 50$, $z(\frac{10}{3},\frac{10}{3})= \frac{110}{3}\approx36.7$ c. maximum $ 60$ at $(0,10)$.
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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 triangular area in the first quadrant. b. With the corner points indicated in the figure, we can find the values of the objective function as $z(0,10)=5(0)+6(10)=60$, $z(10,0)=5(10)+6(0)=50$, $z(\frac{10}{3},\frac{10}{3})=5(\frac{10}{3})+6(\frac{10}{3})=\frac{110}{3}\approx36.7$, c. We can determine that the maximum value of the objective function is $z(0,10)=60$, which occurs at $(0,10)$.
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