Process $x$ has fixed costs of $$11,000$ and variable costs of $$2\mathrm{.}40$ per unit. Process $Y$ has fixed costs of $$9,000$ and variable costs of $$2\mathrm{.}1$ per unit. Which of the following statements is TRUE?

Process $x$ is more profitable than process $Y$ and should be selected.

The crossover point is approximately $6667$ units.

Process $Y$ is cheaper than process $x$ at all volumes.

Process $x$ should be selected for very large production volumes.

It is impossible for one process to have both of its costs lower than those of another process.