To find the maximum profit, we need to find the vertex of the parabolic function P(t) = -4t^2 + 32t - 52.
The x-coordinate of the vertex of a parabola given by the equation y = ax^2 + bx + c is calculated by the formula x = -b/2a.
In this case, a = -4 and b = 32, so the x-coordinate of the vertex is:
t = -32 / 2(-4) = -32 / -8 = 4
Now, we substitute t = 4 back into the original equation to find the maximum profit:
P(4) = -4(4)^2 + 32(4) - 52
P(4) = -4(16) + 128 - 52
P(4) = -64 + 128 - 52
P(4) = 64 - 52
P(4) = 12
So, the maximum profit that can be made is $12,000.
The function P (t) = - 4t^2 + 32l - 52 gives the profit in thousands of producing l units of lip gloss. What is the maximum profit that can be made?
12,000
4,000
208,000
32,000
1 answer