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: 36


a) $C(x)=4.75x+500.000$; b) $b=500.000$; c) $975.000$; d) $4.75$

Work Step by Step

a) Since the cost function is linear, it can be expressed in the form $C(x)=mx+b$ To find each elements in the formula $m=\frac{p_2-p_1}{x_2-x_2}=\frac{737.500-547.500}{50.000-10.000}=4.75$ $p-p_1=m(x-x_1)$ $C(x)-547.500=4.75(x-10.000)$ $C(x)=4.75x+500.000$ b) $C(x)=mx+b$ with $b$ is a fixed cost So $b=500.000$ c) with $x=100.000$ $C(100.000)=4.75(100.000)+500.000=975.000$ d) $C(x)=mx+b$ with $m$ is the marginal cost so The marginal cost is $4.75$
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