Explanation Given information: The John Deere Company has found that the revenue in dollars, from the sales of riding mowers is a function of the unit price p in dollars, that it charges. Revenue function is R ( p ) = − 1 2 p 2 + 1900 p . Explanation: Consider the revenue function R ( p ) = − 1 2 p 2 + 1900 p . Compare it to the standard quadratic function R ( p ) = a p 2 + b p + c . Then, a = − 1 2 , b = 1900 and c = 0 a = − 1 2 < 0 , therefore the graph of R opens down, so the vertex is a maximum point. The x coordinate of the vertex is h = − b 2 a Plug a = − 1 2 , b = 1900 h = − 1900 2 ( − 1 2 ) = 1900

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ISBN: 9780321979070

Author: Michael Sullivan

Publisher: PEARSON

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Chapter 3.3, Problem 86AYU

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The unit price p charged by the John Deere company that maximize revenue and find the maximum revenue, where the revenue function is R(p)=−12p2+1900p.

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Chapter 3.3, Problem 85AYU

Chapter 3.3, Problem 87AYU

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The unit price p charged by the John Deere company that maximize revenue and find the maximum revenue, where the revenue function is R ( p ) = − 1 2 p 2 + 1900 p .

Solution Summary: The John Deere Company has found that the revenue from the sales of riding mowers is a function of the unit price p in dollars, that it charges.

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The unit price p charged by the John Deere company that maximize revenue and find the maximum revenue, where the revenue function is R(p)=−12p2+1900p.

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