This is what the process looks like.
1. The capacity of the system is based on the output of the bottleneck. The bottleneck is the oven, which can process 60min/10min = 6 dozen orders per hour. This assumes one-dozen order sizes.
2. The throughput time is the sum of the processing times for each of the steps. This equals 8+10+5+2+1=26 minutes.
3. In a four-hour shift you can produce the hourly capacity for each hour. This means that you can produce 4*6=24 dozen in the four hours. However, you have a startup time of 8 minutes and a cleanup time of 8 minutes that must be taken away from the four hours. Thus, you have 60min*4hours= 240 minutes – 16 minutes = 224 minutes (3.73 hours) of available processing time. This means that you can produce 3.73*6 = 22.4 dozen per hour. Rounding down is fine here.
4. You are working 6+2 minutes for each dozen. Over the hour, you do this 6 times so you are working 48 minutes. Your utilization would be 48/60=80%. Your roommate is working 1+2+1 = 4 minutes per dozen. So, 4*6=24 minutes per hour. Your roommate’s utilization would be 24/60=40%.
5. Assuming 6 dozen per hour you can gross 6*5=$30. The material expense is 6*(.1+.6)=$4.20. This leaves $25.80 for you and your roommate.
6. You can do this alone. This would mean that you would have to take over your roommates responsibilities of 4 minutes per dozen. Your new total time would be 12 minutes per order. However, this would mean that you are now the bottleneck of the operation. The new capacity based on your new time is 60/12 = 5 dozen cookies per hour. -----------------------
1 min per dozen-
60 dozen per hour
2 min per dozen-
30 dozen per hour
5 min per dozen-
12 dozen per hour
10 min per dozen-
6 dozen per hour
6 + 2 min per dozen-
7.5 dozen per hour
Wash, mix, spoon