Question

The function P(L) = −4L^2+12L +25
gives the profit in thousands of producing L
units of lip gloss. What is the maximum profit that can be made? (1 point)

4,000

34,000

68,000

25,000

Answer 1

The maximum occurs at the vertex: L = −b/(2a) = −12/(2·−4) = 1.5.
P(1.5) = −4(1.5)^2 + 12(1.5) + 25 = −9 + 18 + 25 = 34 (thousand).

So the maximum profit is 34,000.