Explanation Given: The daily profit P in dollars of Pine Tree Picnic Tables in the summer months is described by the function: P ( x ) = − 5 x 2 + 300 x − 4000 where x is the number of tables that are manufactured in one day. Formula used: For graphing the quadratic equation , f ( x ) = a x 2 + b x + c , a ≠ 0 : The coordinates of the vertex are ( − b 2 a , f ( − b 2 a ) ) . Calculation: The maximum profit occurs at the vertex of the parabola, P ( x ) = − 5 x 2 + 300 x − 4000 . Since a = − 5 , b = 300 , and c = − 4000

8th Edition

ISBN: 9780134178967

Author: John Tobey Jr., Jeffrey Slater, Jamie Blair, Jenny Crawford

Publisher: PEARSON

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Chapter 8.5, Problem 33E

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To calculate: The number of tables should be made per day to obtain the maximum profit and find the maximum profit if the profit function is P(x)=−5x2+300x−4000.

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Chapter 8.5, Problem 32E

Chapter 8.5, Problem 34E

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The number of tables should be made per day to obtain the maximum profit and find the maximum profit if the profit function is P ( x ) = − 5 x 2 + 300 x − 4000 .

Solution Summary: The author calculates the daily profit P in dollars of Pine Tree Picnic Tables in the summer months by the function: P(x)=-5x+300x-4000.

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To calculate: The number of tables should be made per day to obtain the maximum profit and find the maximum profit if the profit function is P(x)=−5x2+300x−4000.

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Chapter 8 Solutions