A firm is considering three capacity alternatives: A$,$ B$,$ and C$.$ Alternative A would have an annual fixed cost of $$100,000$ and variable costs of $$22$ per unit. Alternative B would have annual fixed costs of $$120,000$ and variable costs of $$20$ per unit. Alternative C would have fixed costs of $$80,000$ and variable costs of $$30$ per unit. Revenue is expected to be $$50$ per unit. Which alternative will produce the highest profits for an annual output of $10,000$ units?

$$ a$.$ Alternative B

b$.$ Alternative $A$

c$.$ Alternative C

d$.$ A and $B$

e$.$ B and C