A machine does three setups per production cycle. Each setup takes 20 minutes. The processing time is 0.5 minute. What batch size achieves a capacity of 24 units per hour

A batch size of 30units

Explanation:

The set up time is given as 20 Minutes per production cycle, Production cycle  for the machine has 3 cycles

Therefore  the set uo time for the cycles = 20 mins x 3= 60 minutes

Processing time = 0.5 minutes

Capacity = 24units per hour , changing to minutes we have

24 units / 60 minutes = 6/ 15 = 2/5 = 0.4 minutes

Capacity = Batch size / Set up time + batch size x processing  time per unit

0.4 = B/ 60 + B X 0.5

0.4 = B/60 + 0.5B

0.4( 60 + 0.5B) = B

24 + 0.2B=B

24=B-0.2B

0.8B=24

B =24/0.8

Batch size = 30  can be achieve at a capacity of 24 units per hour.