Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Review - Test - Page 235: 5

Answer

a) $R(2)=4000$ dollars $R(4)=4000$ dollars These values represent profit when setting the bars at \$$2$ and \$$4$, respectively. b) There will always be a positive revenue, but there is not a constant proportion between the price of a chocolate bar and the total revenue. c) The maximum revenue is \$$4500$ when pricing the chocolate bar at \$$3$ per bar.

Work Step by Step

a) $R(2)=-500(2)^2+3000\cdot2=$ $-500\cdot4+6000=$ $-2000+6000=4000$ dollars $R(4)=-500(4)^2+3000\cdot4=$ $-500\cdot16+12000=$ $-8000+12000=4000$ dollars b) One can see when graphing the equation that as the price of the chocolate increases from zero, the revenue increases as well until the price of a chocolate bar is \$$3$. When pricing above that, the revenue starts to decline. c) The maximum revenue is represented by the top of the crest that forms in the function.
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