Explanation Given marginal price is. p ′ ( x ) = 0.001 e 0.01 x . d d x ( p ( x ) ) = 0.001 e 0.01 x Use variable separable method and integrate the differential equation to get the price-supply equation d ( p ( x ) ) = 0.001 e 0.01 x ∫ d ( p ( x ) ) = ∫ 0.001 e 0.01 x d x p ( x ) = ∫ 0.001 e 0.01 x d x Let u = 0.01 x , then d u = 0.01 d x . The above equation becomes, p ( x ) = 0.001 ∫ e u 1 0.01 d u . p ( x ) = 0.001 0.01 ∫ e u d u = 0.1 ∫ e u d u = 0.1 e u + C Since u = 0.01 x , the above integral becomes p ( x ) = 0.1 e 0.01 x + C . Given that the supplier is willing to supply 100 tubes per week at a price of $3.65 each. That is, p ( 100 ) = 3.65 . Substitute x = 100 and p ( 100 ) = 3.65 in p ( x ) = 0.1 e 0.01 x + C to find the constant C . p ( 100 ) = 0

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

13th Edition

ISBN: 9780321869838

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen

Publisher: PEARSON

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Chapter 5.2, Problem 7MP

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To find: The price supply equation and the number of tubes the supplier willing to supply at a price of $3.98 each.

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Chapter 5.2, Problem 6MP

Chapter 5.2, Problem 1E

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Chapter 5 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

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The price supply equation and the number of tubes the supplier willing to supply at a price of $3.98 each.

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To find: The price supply equation and the number of tubes the supplier willing to supply at a price of $3.98 each.

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Chapter 5 Solutions