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.

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

Step-by-step 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.