Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 10 - Systems of Equations and Inequalities - Chapter Review - Review Exercises - Page 815: 52

Answer

minimum $z=3$ at $(1,0)$.

Work Step by Step

1. See graph for $\begin{cases}x\ge0\\y\ge0\\x+y\ge1\\3x+2y\le12\\ x+3y\le12 \end{cases}$ 2. Identify the corner(s) as $\left(0,1\right),\left(1,0\right)\left(4,0\right),\left(0,4\right),\left(\frac{12}{7},\frac{24}{7}\right)$ 3. Evaluate the expression $z=3x+5y$ at the above corners as $z=5,3,12,20,\frac{156}{7}$ 4. Thus the minimum is $z=3$ at $(1,0)$.
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