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: 18


4 oz Food-A and 2 oz Food-B.

Work Step by Step

Step 1. Assume $x$ ounces of Food-A and $y$ ounces of Food-B are needed. Step 2. Based on the given conditions, the total cost can be written as $z(x,y)=0.12x+0.08y$ dollars Step 3. We can convert the constraints into inequalities as $\begin{cases} x+y\geq6\\x+y\leq7\\2x+y\geq10 \end{cases}$ Step 4. Graph the above inequalities; we can find the vertices and the solution region as a four-sided area. Step 5. With the objective equation and vertices, we have $z(6,0)=0.12(6)+0.08(0)=0.72$, $z(7,0)=0.12(7)+0.08(0)=0.84$, $z(3,4)=0.12(3)+0.08(4)=0.36+32=0.68$, $z(4,2)=0.12(4)+0.08(2)=0.64$ Step 6. Based on the above results, we can find the minimum cost as $z(4,2)= 0.64$ dollars with servings of 4 oz Food-A and 2 oz Food-B.
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