$($Purchasing$)$ A company has to make a choice between two alternate suppliers. Supplier Alpha will charge a fixed amount of $$10,000$ and thereafter, a variable cost of $$2\mathrm{.}40$ per unit. Supplier Beta will charge a fixed amount of $$9,000$ and thereafter, a variable cost of $$2\mathrm{.}25$ per unit. Which of the following statements is TRUE?

Group of answer choices

The crossover point between Supplier Alpha and Beta is approximately $6667$ units.

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

Supplier Beta is cheaper than Supplier Alpha at all volumes.

Supplier Alpha should be selected for very large production volumes.

Supplier Alpha is more profitable than Supplier Beta and should be selected.