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: 23

Answer

$C(x)=30x+100$

Work Step by Step

Assuming a linear cost function, $C(x)=mx+b$, where m represents the marginal cost and b represents the fixed cost. Here, b= $\$ 100$ (fixed cost) and m= $?$ (the cost to produce one item). Let $C(x)=$ cost of producing $x$ items. $C(x)=mx+100$ We don't know m, but we were given $C($50$)=1600$ , so we solve (for m): $m(50)+100=1600$ $50m=1500\qquad/\div 50$ $m=30$. So, $C(x)=30x+100$
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