$(15$ points total$)$ 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 tabulated below.

FC

Rev

VC

A

$$40,000$

$$15/$unit

$$10/$unit

B

$$30,000$

$$15/$unit

$$11/$unit

$(6$ points$)$ Determine the break$-$even point of each alternative.

$(5$ points$)$ At what volume of output would the two alternatives yield the same profit?

$(4$ points$)$ If the expected demand is $12,000$ units, which alternative would yield the higher profit?