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 5,000 5,000 20,000 20,000 9,000 9,000 41,000
To find the number of lip glosses that need to be produced to maximize profits, we need to find the maximum of the quadratic function P(l) = −2l^2 + 20l −9.
The maximum point of a quadratic function in the form P(l) = al^2 + bl + c occurs at l = -b/(2a). In this case, a = -2 and b = 20.
l = -20/(2*(-2))
l = -20/(-4)
l = 5
Therefore, the number of lip glosses that need to be produced to maximize profits is 5,000.