The function P (l) = -2l^2 + 20l - 9 gives the profit of producing l lip glosses in thousands. How many lip glosses need to be produced to maximize profits?

Question

a. 9,000
b. 41,000
c. 5,000
d. 20,000

Answer 1

To find the number of lip glosses that need to be produced to maximize profits, we need to find the vertex of the parabola represented by the profit function P(l) = -2l^2 + 20l - 9.

The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a = -2 and b = 20 in this case.

x = -20 / (2*-2) = -20 / -4 = 5

So, the maximum profit is achieved when l = 5.

Therefore, the correct answer is:

c. 5,000