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?

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

1 answer

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

The x-coordinate of the vertex is given by the formula x = -b / 2a. In this case, a = -2 and b = 20.

Therefore, x = -20 / (2*(-2)) = -20 / -4 = 5.

So, the number of lip glosses that need to be produced to maximize profits is 5,000.

Therefore, the answer is:

c. 5,000