Question 7: An LED manufacturer determines that in order to sell x nu…

An LED manufacturer determines that in order to sell $x$ number of LEDs, the price per LED(in thousands) must be $f(x) = 1000 - x$, if $x \leq 800$, and the manufacturer also determines that the total cost(in thousands) of producing $x$ number of LEDs is

$g(x) = \begin{cases} 30000 + 300x & \text{if } x \leq 400, \\ 100x + 110000 & \text{if } 400 < x \leq 800 \end{cases}$

Although in the above context, $x$ can take only integer values, assume that $x$ is a continuous variable in the interval $[0, 800]$ and that the functions $f(x)$ and $g(x)$ are defined as above on this entire interval.

Let $P(x)$ denote the function representing the profit of the company. Choose the set of correct statements.