Explanation Given information: A farmer uses x lb. of fertilizer per acre at a cost of $2 per pound, leading to a revenue of R = 700 − 400 e − x 100 dollars per acre. Formula used: The profit π ( q ) is the difference between the revenue, R ( q ) , and the cost, C ( q ) , of supplying that quantity. ⇒ π ( q ) = R ( q ) − C ( q ) Calculation: R = 700 − 400 e − x 100 The farmer uses x lb. of fertilizer per acre at a cost of $2 per pound. ⇒ C ( x ) = 2 x The profit is π ( x ) = R ( x ) − C ( x ) ⇒ π ( x ) = ( 700 − 400 e − x 100 ) − 2 x Differentiating with respect to ‘x’, we get π < To determine (b) To calculate: The maximum profit on a 200 acre farm.

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 4.4, Problem 23P

To determine

(a)

To calculate:

The number of pounds of fertilizer should be applied per acre to maximize profit.

To determine

(b)

To calculate:

The maximum profit on a 200 acre farm.

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Chapter 4.4, Problem 22P

Chapter 4.4, Problem 24P

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Applied Calculus, 6e WileyPLUS + Loose-leaf

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(a) To calculate: The number of pounds of fertilizer should be applied per acre to maximize profit.

Solution Summary: The author calculates the number of pounds of fertilizer to be applied per acre to maximize profit.