Explanation Given: The price of first 250 tables is $160 per table. There is a reduction of 50 percent on the entire order for each additional table that exceeds 250 have 50 percent Calculation: Let x be the number of additional tables. Then the number of tables ordered is 250 + x and cost per table is 160 − 0.50 x The revenue is product of number of tables and cost of each table. Revenue R ( x ) = ( 160 − 0.50 x ) ( 250 + x ) = 40 , 000 − 125 x + 160 x − 0.5 x 2 = 40 , 000 + 35 x − 0.5 x 2 The first derivative of R ( x ) is given by, R ′ ( x ) = d d x ( 40 , 000 + 35 x − 0.5 x 2 ) = 35 − ( 0.5 ) ( 2 x ) = 35 − x The second derivative of R ( x ) is as follows, R ″ ( x ) = d d x ( 35 − x ) = − 1 < 0 Since R ″ ( x ) < 0 , the revenue is maximum at R ′ ( x ) = 0

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 6.2, Problem 18E

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To find: The maximum and minimum revenue.

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Chapter 6.2, Problem 17E

Chapter 6.2, Problem 19E

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Calculus with Applications (11th Edition)

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