Explanation Given: The price of the carpet per square foot is $5. The length of the carpet is a multiple of half foot. Number of carpets sold is 100 when the carpet size is 2 ft by 2 ft. The length and width of the each additional foot, the sold number goes down by 6. Calculation: Let x be the number of feet over the minimum size of the carpet. From the given information, the total number of feet sold is ( 100 − 6 x ) The size of the carpet is ( 2 + x ) . The carpets are in square shape. So, the area is ( 2 + x ) 2 . The price of the carpet per square foot is $5. Thus, the revenue is given by r ( x ) = ( 100 − 6 x ) ( 2 + x ) 2 ( 5 ) = ( 500 − 30 x ) ( 4 + x 2 + 4 x ) = 2000 + 500 x 2 + 2000 x − 120 x − 30 x 3 − 120 x 2 = − 30 x 3 + 380 x 2 + 1880 x + 2000 Differentiate r ( x ) with respect to x , r ′ ( x ) = − 30 ( 3 ) x 2 + 380 ( 2 ) x + 1880 = − 90 x 2 + 760 x + 1880 = ( − 10 ) ( 9 x 2 − 76 x − 188 ) = ( − 10 ) ( x + 2 ) ( 9 x − 94 ) Thus, the values, x = − 2 and x = 94 9 ≈ 10

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

11th Edition

ISBN: 9780133886832

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

Publisher: PEARSON

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Chapter 6.2, Problem 27E

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To find: The size of the carpet which give the maximum monthly revenue.

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Chapter 6.2, Problem 26E

Chapter 6.2, Problem 28E

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Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

Ch. 6.1 - YOUR TURN 1 Find the absolute extrema of the...Ch. 6.1 - Prob. 2YT Ch. 6.1 - Prob. 1WE Ch. 6.1 - Prob. 2WE Ch. 6.1 - Prob. 1E Ch. 6.1 - Find the locations of any absolute extrema for the...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

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