he function P(l) = −4l2 +32l − 52
gives the profit in thousands of producing l
units of lip gloss. What is the maximum profit that can be made? (1 point)
Responses
12,000
12,000
4,000
4,000
208,000
The maximum profit can be found by taking the derivative of the profit function and setting it equal to 0.
P'(l) = -8l + 32
-8l + 32 = 0
-8l = -32
l = 4
Therefore, the maximum profit occurs when 4 units of lip gloss are produced.
P(4) = -4(4)^2 + 32(4) - 52
P(4) = -4(16) + 128 - 52
P(4) = -64 + 128 - 52
P(4) = 12
So the maximum profit that can be made is $12,000.
Therefore, the correct answer is 12,000.