Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 1 - Linear Functions - 1.2 Linear Functions and Applications - 1.2 Exercises - Page 24: 34


a. $m=2.15$; b. $187.5$ books; c. $545$ books

Work Step by Step

a. The total cost $C(x)$ in dollars of producing and selling $x$ units is given by $C(x)=mx+b$ with $x=1000, b=525, mx+b=2675$ we have $C(1000)=m(1000)+525=2675$ $1000m=2150$ $m=2.15$ b. Since $R(x)=px$ and $p=\$4.95$, $R(x)=4.95x$ Substituting for $R(x)$ and $C(x)$ in the equation $R(x)=C(x)$ gives $C(x)=R(x)$ $2.15x+525=4.95x$ $2.8x=525$ $x=187.5$ c. Let $P(x)=1000$ in the equation $P(x)=4.95x-(2.15x+525)$ $1525=2.8x$ $x \approx 544.6 \approx 545$
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