Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 1 - Section 1.3 - Linear Functions and Models - Exercises - Page 91: 80

Answer

Daily fixed cost = $\$ 3000$ Marginal cost = $\$ 5$ per case

Work Step by Step

$C(x)=mx+b$ is called a linear cost function. {\it T}he variable cost is $mx$ and the fixed cost is $b$. The slope $m$, the marginal cost, measures the incremental cost per item. With the given information, we observe two points on the graph of the cost function: $(1000,6000)$ and $(1500,8500)$. Calculate the slope: $m=\displaystyle \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8500-6000}{1500-1000}=\frac{2500}{500}=5$ (Marginal cost = $\$ 5$ per case) The cost function has form $C(x)=$5$x+b.$ To find b, substitute the coordinates of $(1000,6000)$ and solve for $b.$ $6000=5(600)+b$ $6000=3000+b\qquad/-3000$ $3000=b$ (the daily fixed cost is $\$ 3000$)
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