A product can be manufactured at a total cost , where is the number of units produced. The price at…

A product can be manufactured at a total cost $C(x) = \frac{x^2}{100} + 100x + 40$, where $x$ is the number of units produced. The price at which each unit can be sold is given by $P = \left(200 - \frac{x}{400}\right)$. Determine the production level $x$ at which the profit is maximum. What is the price per unit and total profit at the level of production?