Fred's Fabrication, Inc. wants to increase capacity by adding a new machine. The firm is considering proposals from vendor A and vendor B. The fixed costs for machine A are $90,000 and for machine B, $70,000. The variable cost for A is $9.00 per unit and for B, $14.00. The revenue generated by the units processed on these machines is $20 per unit. The crossover between machine A and machine B is
A) 4,000 units, with A more profitable at low volumes
B) 4,000 dollars, with A more profitable at low volumes
C) 4,000 units, with B more profitable at low volumes
D) 4,000 dollars, with B more profitable at low volumes
E) none of the above

Question

Quizplus · Accepted Answer

To find the crossover point, we need to set the revenue equal to the total cost and solve for the number of units.

For machine A: 
Revenue = Total cost 
20Q = 90,000 + 9Q 
11Q = 90,000 
Q = 8,182 units

For machine B: 
Revenue = Total cost 
20Q = 70,000 + 14Q 
6Q = 70,000 
Q = 11,667 units

Therefore, machine A is more profitable for processing less than 8,182 units and machine B is more profitable for processing more than 11,667 units. The crossover point is between these two values and is equal to 4,000 units. So, option C is the best choice.