A company sells square carpets for $55 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 100100 carpets in a week when the carpets are 33 ft by 33 ft, the minimum size. Beyond this, for each additional foot of length and width, the number sold goes down by 55. What size carpets should the company sell to maximize its revenue? What is the maximum weekly revenue?

Complete Question:

A company sells square carpets for $5 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 100 carpets in a week when the carpets are 3 ft by 3 ft, the minimum size. Beyond this, for each additional foot of length and width, the number sold goes down by 5. What size carpets should the company sell to maximize its revenue? What is the maximum weekly revenue?

1. The size carpets of 3 ft by 3 ft will maximize the company's revenue.  This is also the minimum size.  This is more so given that "for each additional foot of length and width, the number of sales goes down by 5."

2. The maximum weekly revenue:

The maximum weekly sales revenue

= $45 x 100

= $4,500

Explanation:

a) Data and Calculations:

3" x 3" = 9 squared feet

1 squared foot sells for $5

Therefore, 9 squared feet will sell for $45 ($5 x 9)

Maximum number of sales = 100 carpets per week

Therefore, the maximum sales revenue = $45 x 100 = $4,500

b) To maximize company revenue, this company must sell the highest number of carpets possible and not less.  If this company increases the size of the carpet beyond the minimum, sales will reduce by 5, according to the information provided.  However, there was no indication that the reduced sales will result to increased price per carpet.