Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 1 - Review - Exercises - Page 69: 24

Answer

(a) $C = 6x+3000$ (b) The slope of the graph is 6 It represents the cost to manufacture each oven. (c) The y-intercept is 3000. It represents the fixed costs for the manufacturer.

Work Step by Step

(a) It costs $\$9000$ to produce 1000 ovens. It costs $\$12,000$ to produce 1500 ovens. We can find the slope: $m = \frac{12,000-9000}{1500-1000} = \$6/oven$ We can find the y-intercept: $y = mx+b$ $9000 = 6(1000)+b$ $b = \$3000$ Let $x$ be the number of ovens that are manufactured. We can write the cost function: $C = 6x+3000$ (b) The slope of the graph is 6. This slope is $\$6/oven$, and it represents the cost to manufacture each oven. (c) The y-intercept is 3000. This is $\$3000$ and it represents the fixed costs for the manufacturer. That is, $\$3000$ is the cost the manufacturer has to pay even if they don't manufacture any ovens.
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