Question

A profit function is derived from the production cost and revenue function for a given item. The monthly profit function for a certain item is given by P(x)=−0.05x^2+400x−100,000, where P is in dollars and x is the number of units sold.

a. How many units must be sold on a monthly basis to maximize the profit?

b. Find the maximum profit

Answer 1

as you recall, the parabola

ax^2+bx+c has its vertex at

x = -b/2a

so, plug that in and use that to get part (b)