Question

Luci Lulu opened a cookie store in the mall. She found that the relationship between the price of a cookie, p, and the number of cookies sold, x, is given by the linear relationship x= -2000 p + 4000. Find the maximum revenue Luci can make selling cookies in one day. Find the price she should sell the cookies for to make the maximum revenue.

Answer 1

The maximum revenue Luci can make selling cookies in one day is $2,000.

The price she should sell the cookies to make the maximum revenue is $1

Explanation:

W are given the following in the question:

x= -2000 p + 4000 ................ (1)

Therefore, revenue can be obtained as follows:

Revenue = R = px = p(-2000 p + 4000) = -2000p^2 + 4000p ........... (2)

Differentiating equation (2) with respect to p and equate to 0, we have:

dR / dp = -4000p + 4000 = 0 ................. (3)

From equation (3), we solve for p as follows:

-4000p + 4000 = 0

4000 = 4000p

p = 4000 / 4000

p = 1

Therefore, this implies that the price she should sell the cookies to make the maximum revenue is $1.

Substituting p = 1 into (2), we have:

Revenue = (-2000 * 1^2) + (4000 * 1)

Revenue = -2000 + 4000

Revenue = 2000

Therefore, this implies that the maximum revenue Luci can make selling cookies in one day is $2,000.