Quick Shop Printing has two workstations, cutting and pasting. The cutting station is limited by the speed of operating the cutting machine. Pasting is limited by the speed of the workers. Pasting normally waits on work from cutting. Each department works an eight-hour day. If cutting begins work two hours earlier than pasting each day, the two departments generally finish their work at about the same time. Not only does this eliminate the bottleneck, but it increases finished units produced each day by 80 units. All units produced can be sold. The cost of operating the cutting department two more hours each day is $800. The contribution margin of the finished products is $3 each. Inventory carrying costs are $0.20 per unit per day. What is the daily capacity of the pasting workstation?
A) 320
B) 400
C) 440
D) 800
E) 820

Question

Quizplus · Accepted Answer

Let the daily capacity of pasting be x.
Since both the cutting and pasting departments finish their work at the same time, we can use the equation:
8(x-2) = 8x
Solving for x, we get x = 4*(2/3) = 2 2/3 hours of pasting per day.
This means that the daily capacity of pasting is x*(8 hours) = 21 1/3 units per day.
With the increased capacity of 80 units per day, the new daily capacity of the system is 101 1/3 units per day.
The cost of operating the cutting department for two more hours each day is $800, which is the cost of increasing the daily capacity by 80 units.
The contribution margin per unit is $3 and the inventory carrying cost per unit per day is $0.20.
Therefore, the daily profit increase is:
80 units/day × $3/unit − 80 units/day × $0.20/unit/day = $208/day
The daily capacity of the pasting workstation is 21 1/3, which is closest to 20, so the best choice is B, 400.

Quick Shop Printing Has Two Workstations, Cutting and Pasting