SOLUTION: 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 reve

Question 1063304: 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 $40,000 for A and $30,000 for B; variable costs per unit
would be $10 for A and $11 for B; and revenue per unit would be $15.
a. Determine each alternative�s break-even point in units.
b. At what volume of output would the two alternatives yield the same profit?
c. If expected annual demand is 12,000 units, which alternative would yield the higher profit?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
break-even for a is 40,000+10x=15x
5x=40,000; x=8000 units.
break-even for b is 30,000+11x=15x
4x=30,000; x=7500 units.
----------------------
same profit when 40,000+10x=30,000+11x
x=10,000 units
A will make 150,000-40,000-100,000=10,000
B will make 150,000-30,000-110,000=10,000
---------------------
at 12,000
a will make 180,000-40,000-120,000=20,000
b will make 180,000-30,000-132,000=18,000
a will yield more profit, which makes sense, because variable costs are now less and fixed costs have been recovered.
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