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: 21


100 parents and 50 students.

Work Step by Step

Step 1. Assume $x$ number of parents and $y$ number of students. Step 2. Based on the given conditions, the total amount of money raised can be written as $z(x,y)=2x+ y$ Step 3. We can convert the constraints into inequalities as $\begin{cases} x\geq0,y\geq0\\ x+y\leq150\\\frac{x}{2}\leq y \end{cases}$ Step 4. Graphing the above inequalities, we can find the vertices and the solution region as a triangular area in the first quadrant. Step 5. With the objective equation and vertices, we have $z(0,0)=2(0)+(0)=0$, $z(100,50)=2(100)+(50)=250$, $z(0,150)=2(0)+(150)=150$, Step 6. Based on the above results, we can find the maximum as $z(100,50)=250$ dollars with 100 parents and 50 students.
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