The function P(l) = −2l2+ 20l −9
gives the profit of producing l
lip glosses in thousands. How many lip glosses need to be produced to maximize profits? (1 point)
Responses
41,000
41,000
9,000
9,000
5,000
5,000
20,000
20,000
The function for profit is given by P(l) = -2l^2 + 20l - 9.
To find the number of lip glosses needed to maximize profits, we need to find the vertex of the parabola given by this quadratic function.
The vertex of a parabola in the form of y = ax^2 + bx + c is located at x = -b/(2a). In this case, since l represents the number of lip glosses, we're looking for the value of l at the vertex.
For P(l) = -2l^2 + 20l - 9, a = -2 and b = 20. Plug these values into x = -b/(2a) to find the number of lip glosses needed to maximize profits:
l = -20/(2*(-2)) = -20/(-4) = 5
Therefore, the number of lip glosses that need to be produced to maximize profits is 5,000.
Answer: 5,000