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 873: 17


40 Model-A and 0 Model-B bikes.

Work Step by Step

Step 1. Assume $x$ number of Model-A and $y$ number of Model-B are produced. Step 2. Based on the given conditions, the total profit can be written as $z(x,y)=25x+15y$ Step 3. We can convert the constraints into inequalities as $\begin{cases} 5x+4y\leq200\\2x+3y\leq108 \end{cases}$ Step 4. See graph for the vertices and the solution region as a four-sided area. Step 5. With the objective equation and vertices, we have $z(0,0)=25(0)+15(0)=0$, $z(0,36)=25(0)+15(36)=540$, $z(24,20)=25(24)+15(20)=900$, $z(40,0)=25(40)+15(0)=1000$ Step 6. Based on the above results, we can find the maximum profit as $z(40,0)= 1000$ dollars by producing 40 Model-A and 0 Model-B bikes.
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