What’s the maximum profit?

Question

Find the maximum profit if the equation of profit is p(x)=2+8x-x^2, where p(x) is the profit and x is the number of products sold.

Answer 1

TO find the maximum profit, we are going to find the maximum point of this function. To do this, we will find the vertex.

First we will find the x-value of the vertex by using the formula:

-b / (2a)

You can find a and b by using the standard form of a quadratic functions:

ax² + bx + 6

Now, look at the function given. The coefficient attached to the x² is your a and the coefficient attached to the x is your b:

a = -1 b = 8

Now plug this into the equation:

-8 / (2*-1) = -8 / -2 = 4

So our x-value is 4. Now to find the profit p(x), plug 4 in for x and solve:

p(4) = 2 + 8(4) - (4)²

p(4) = 2 + 32 -16

p(4) = 18

So the max profit is $18.

I hope this explanation was thorough and answered all of your questions. If you have additional questions please don't hesitate to reach out. Learn on! :)