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

Answer 1

The maximum revenue Luci can make selling cookies in one day is $4,004,000.

Explanation:

Given;

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

Revenue = xp

Revenue = (−2000 p + 4000)p =

Revenue = −2000p^2 + 4000p .................... (2)

The price at which Luci will the maximum profit can be calculated by finding the derivative of equation (2), equating to 0, and then solve for p as follows:

−4000p + 4000 = 0

4000 = 4000p

p = 4000 / 4000

p = 1

This implies that the price at which Luci will the maximum profit is $1.

Substituting p = 1 into equation (2) to obtain the maximum revenue Luci can make selling cookies in one day, we have:

Revenue = (−2000 * 1)^2 + (4000 * 1)

Revenue = −2000^2 + 4000

Revenue = 4,000,000 + 4000

Revenue = 4,004,000

Therefore, the maximum revenue Luci can make selling cookies in one day is $4,004,000.