A company sells square carpets for $7 per square foot. It has a simplified manufacturing process for which all the carpets each week must be the same size, and the length must be a multiple of a half foot. It has found that it can sell 200 carpets in a week when the carpets are 2 ft by 2 ft, which is the minimum size. Beyond this, for each additional foot of length and width, the number sold goes down by 3. a. Write the equation for the revenue, R, the company will earn as a function of the length, x, of the carpet squares sold. b. What size carpets should the company sell to maximize its weekly revenue? c. What is the maximum weekly revenue?

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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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13. A company sells square carpets for $7 per square foot. It has a simplified manufacturing process for which all the
carpets each week must be the same size, and the length must be a multiple of a half foot. It has found that it
can sell 200 carpets in a week when the carpets are 2 ft by 2 ft, which is the minimum size. Beyond this, for each
additional foot of length and width, the number sold goes down by 3.
a. Write the equation for the revenue, R, the company will earn as a function of the length, x, of the carpet
squares sold.
b. What size carpets should the company sell to maximize its weekly revenue?
What is the maximum weekly revenue?
C.
Transcribed Image Text:13. A company sells square carpets for $7 per square foot. It has a simplified manufacturing process for which all the carpets each week must be the same size, and the length must be a multiple of a half foot. It has found that it can sell 200 carpets in a week when the carpets are 2 ft by 2 ft, which is the minimum size. Beyond this, for each additional foot of length and width, the number sold goes down by 3. a. Write the equation for the revenue, R, the company will earn as a function of the length, x, of the carpet squares sold. b. What size carpets should the company sell to maximize its weekly revenue? What is the maximum weekly revenue? C.
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