Question

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?

Answer 1

To maximize revenue, the company should sell the size of carpets that yields the highest number of carpets sold. The size that maximizes revenue is 35 ft by 35 ft, resulting in 99990 carpets sold each week. The maximum weekly revenue is $549,450.

Step-by-step explanation:

To maximize revenue, the company should sell the size of carpets that yields the highest number of carpets sold. Based on the information given, the number of carpets sold decreases by 55 for each additional foot of length and width. To find the size that maximizes revenue, we need to determine the length and width that results in the highest number of carpets sold.

Let's start by determining the number of additional feet of length and width that would maximize revenue. If we divide the decrease in the number of carpets sold (55) by the additional foot of length and width, we get:

(55 / 1) = 55.

So for each additional foot of length and width, the number of carpets sold decreases by 55. Now, let's find the size that yields the highest number of carpets sold. The minimum size is 33 ft by 33 ft. We can start increasing the length and width by adding 1 foot at a time and track the number of carpets sold:

1. 33 ft by 33 ft - 100100 carpets sold
2. 34 ft by 34 ft - 100045 carpets sold
3. 35 ft by 35 ft - 99990 carpets sold
4. 36 ft by 36 ft - 99935 carpets sold

At this point, we can see that the number of carpets sold is decreasing with each additional foot. Therefore, the size that maximizes revenue is 35 ft by 35 ft, resulting in 99990 carpets sold each week.

To find the maximum weekly revenue, we multiply the number of carpets sold (99990) by the price per square foot ($55).

Maximum weekly revenue = 99990 * $55 = $549,450.

Answer 2

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?

Answer:

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

Step-by-step 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.