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Sagot :
Answer:
a. The maximum revenue Luci can make selling cookies in one day is $2,000.
b. The price she should sell the cookies for her to make the maximum revenue is $1.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
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 explanation of the answer is now provided as follows:
Given;
x = −2000p + 4000 …………………………. (1)
The revenue function is obtained as follows:
R = px ……………………….. (2)
Substitute equation (1) into (2), we have:
R = p(−2000p + 4000)
R = −2000p^2 + 4000p ……………… (3)
Obtain the derivative of equation (3), set to zero and solve for p, we have:
−4000p + 4000 = 0
4000 = 4000p
p = 4000 / 4000
p = 1
From the above, p = 1 implies that the price that ensure maximum revenue is $1.
We can now answer as follows:
a. Find the maximum revenue Luci can make selling cookies in one day.
Since p = 1 implies that the price that ensure maximum revenue is $1, we then substitute p = 1 into equation (3) as follows:
R = (−2000 * 1^2) + (4000 * 1)
R = (−2000 * 1) + (4000 * 1)
R = −2000 + 4000
R = 2000
Therefore, the maximum revenue Luci can make selling cookies in one day is $2,000.
b. Find the price she should sell the cookies for to make the maximum revenue.
Since p = 1 implies that the price that ensure maximum revenue is $1 as obtained above, it therefore implies that the price she should sell the cookies for her to make the maximum revenue is $1.
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