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 $$37,000$ for A and $$31,000$ for $B$; variable costs per unit would be $$9$ for A and $$11$ for B ; and revenue per unit would be $$19.$

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

Note: Round your answer to the nearest whole amount.

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b$.$ At what volume of output would the two alternatives yielf the same profit $($or loss$)?$ Note: Round your answer to the nearest whole amount.

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

Higher profit