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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?

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?

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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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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