To find the maximum profit that can be made, we need to find the vertex of the parabola represented by the function P(l) = -5l^2 + 20l + 15.
The vertex of a parabola in the form y = ax^2 + bx + c is given by the formula x = -b / 2a.
In this case, a = -5 and b = 20.
So, the x-coordinate of the vertex is x = -20 / 2*(-5) = -20 / -10 = 2.
Now, we need to find the y-coordinate of the vertex by substituting x = 2 back into the equation P(l) = -5l^2 + 20l + 15.
P(2) = -5(2)^2 + 20(2) + 15
P(2) = -5(4) + 40 + 15
P(2) = -20 + 40 + 15
P(2) = 35
Therefore, the maximum profit that can be made is $35,000.
The correct answer is:
a. 35,000
The function P(l) = -5l^2 + 20l + 15 gives the profit in thousands of producing l units of lip gloss. What is the maximum profit that can be made?
a. 35,000
b. 75,000
c. 2,000
d. 20,000
1 answer