Maximizing Profit for Gadget A

A company produces and sells gadget A. The price of gadget A as a function of the number of units sold, $x$, can be modeled by the equation:

$$ p(x) = -2x + 150 $$

where $p(x)$ is the price in dollars. The company has fixed costs of $200 and a variable cost of $50 per unit produced. The profit $P$ as a function of $x$ can be represented by:

$$ P(x) = p(x) imes x - ext{(fixed costs + variable costs)} $$

What is the maximum profit that the company can achieve?