For a certain product, the total revenue is given by , and the total cost is given by . Write an integral that gives the average profit for the product over the interval from 4 to 11

Question

For a certain product, the total revenue is given by  , and the total cost is given by  . Write an integral that gives the average profit for the product over the interval from 4 to 11 ​

Quizplus · Accepted Answer

The average profit is given by

( total revenue - total cost ) / ( number of units sold )

We need to evaluate this expression over the interval from 4 to 11. Since we don't know the number of units sold, we need to express the total revenue and total cost as functions of the number of units sold.

Let x be the number of units sold. Then, we have

total revenue = 11ea984b_b051_ef11_9029_e9d381c790ac_TB4005_11 = 19x

total cost = 11ea984b_b051_ef12_9029_b16edba2aced_TB4005_11 = 5x^2 - 2x + 14

The profit is

19x - (5x^2 - 2x + 14) = -5x^2 + 21x - 14

So, the average profit over the interval from 4 to 11 is given by

(1/7) * 11ea984b_b052_1624_9029_bf9cb0db2b5b_TB4005_11 = 11ea984b_b052_6446_9029_cd3b8e5a2b05_TB4005_11

which is approximately equal to 2.087.

For a Certain Product, the Total Revenue Is Given by