A small firm intends to increase the capacity of a bottleneck operation by adding a new machine. Two alternatives, A and $B,$ have been

identified, and the associated costs and revenues have been estimated. Annual fixed costs would be $$36,000$ for A and $$31,000$ for $B$;

variable costs per unit would be $$7$ for A and $$11$ for $B$; and revenue per unit would be $$18.$

a$.$ Determine each alternative's break$-$even point in units.

Note: Round your answer to the nearest whole amount.

b$.$ At what volume of output would the two alternatives yield the same profit $($or loss$)?$

Note: Round your answer to the nearest whole amount.

c$.$ If expected annual demand is $15,000$ units, which alternative would yield the higher profit $($or the lower loss$)?$