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)=−0.05x2+500x−100,000, where P is in dollars and x is the number of units sold.

19a. How many units must be sold on a monthly basis to maximize the profit?

19b. Find the maximum profit:

Answer 1

recall how to find the vertex of a parabola. In this case, that will be at

x = -b/2a = 500/0.1

Now use that to find P(x)