A small firm intends to increase the capacity of a bottleneck operation by addin
ID: 398951 • Letter: A
Question
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 $17.
a. Determine each alternative’s break-even point in units. (Round your answer to the nearest whole amount.)
QBEP,A 3600 units
QBEP,B 5167 units
b. At what volume of output would the two alternatives yield the same profit? (Round your answer to the nearest whole amount.)
Profit 53000 units
c. If expected annual demand is 14,000 units, which alternative would yield the higher profit?
Higher profit is A
**The answers are in bold, please correct the answer for answer b please**
Explanation / Answer
a) Given, For A
Annual Fixed Cost :$36000
Variable Cost per unit : $7
Revenue : $17
For B
Annual Fixed Cost : $31000
VC per unit : $11
Revenue : $17
Thus , BEP = Total Fixed Cost / Revenue - Variable Cost per unit
For A, 36000 / 17 - 7
36000 / 10= 3600 units
For B, 31000 /17 -11
= 31000 / 6
= 5167 units
b) Profit = TR - TC
Let the number of units be x
x * 17 - (36000 + x * 7) = x * 17 - (31000 + x*11)
17x - 36000 - 7x = 17x - 31000 - 11x
-7x +11x = -31000 + 36000
4x = 5000
x= 1250 units
The two alternatives yield the same profit at an output of 1250 units.
x = 1250 units
c. Higher Profit is A