In a work center, Machine A has a 10-minute set-up time per batch and a 2-minute per unit run time. Machine B performs the identical function but has a set-up time of 30 minutes and a 1-minute run time per unit. The work center makes products in batches ranging from 1 unit to 100 units. Assuming capacity is not a limitation on either Machine, in order to minimize the total processing time, on which batches should Machine B be used?
A) All batches should be run on Machine B.
B) Batches of more than 20 units should be run on Machine B.
C) Batches of fewer than 80 units should be run on Machine B.
D) Batches with up to 50 units should be run on Machine B.
E) No batches should be run on Machine B.

Question

Quizplus · Accepted Answer

To determine which machine to use, we calculate the total processing time for each machine and compare them. For Machine A, the total time for a batch is 10 minutes (set-up) + 2 minutes/unit * number of units. For Machine B, it's 30 minutes (set-up) + 1 minute/unit * number of units. Machine B becomes more efficient when its total time is less than Machine A's. Setting their equations equal and solving for the number of units gives a break-even point at 20 units. For batches larger than 20 units, Machine B is more efficient due to its lower per unit run time despite its longer set-up time.

In a Work Center, Machine a Has a 10-Minute Set-Up