The profit function for a firm making DVDs is P (x) = 88x - x2 - 1200. Find the number of DVDs at which maximum profit is achieved, and find the maximum profit. Explain your work.

This is a quadratic equation so you are looking for the vertex of the parabola.

The y value is the maximum profit.

p (x) = - x^2 + 88x - 1200

a = - 1, b = 88

x = - b/2a; x = - 88 / (2*-1); x = 44

Plug x back in to the equation to find y.

y = - (44) ^2 + 88 (44) - 1200

y = 736

The number of DVD's sold were 44 for a profit of $736