Question

The profit function for a firm making DVDs is P(x) = 88x - x^2 -1200. Find the number of DVDs at which maximum profit is achieved, and find the maximum profit. Please explain. Thank you!

Answer 1

@peachpi

Answer 2

@Nnesha

Answer 3

Is x the number of dvds?

Answer 4

Yeah I think so.

Answer 5

It looks like this is asking for the vertex of the parabola.
\(x=-\frac{b}{2a}\) is the amount of dvd where profit is max
\(P(-\frac{b}{2a})\) is the maximum profit

Answer 6

Do I plug in the 88 and -1200 in that formula?

Answer 7

-b/(2a) = -88/(2*-1)

Answer 8

a is the coefficient of x²
b is the coefficient of x
c is the constant
It helps to write it in descending order

Answer 9

44 so that would be the max number of dvds

88(44)-44^2-1200=$736 (the max profit)

Answer 10

@peachpi thank you :)

Answer 11

that's what I got :) you're welcome