## KJ4UTS one year ago 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!

1. KJ4UTS

@peachpi

2. some.random.cool.kid

@Nnesha

3. anonymous

Is x the number of dvds?

4. KJ4UTS

Yeah I think so.

5. anonymous

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

6. KJ4UTS

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

7. anonymous

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

8. anonymous

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

9. KJ4UTS

44 so that would be the max number of dvds 88(44)-44^2-1200=\$736 (the max profit)

10. KJ4UTS

@peachpi thank you :)

11. anonymous

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