This should be really simple but I'm getting stuck and I'm probably extremely dumb..
I know that a machine receives two kind of parts:
Type 1 -> with frequency 50 per week, each one is processed for 20 minutes Type 2 -> with frequency 100 per week, each one is processed for 8 minutes
It was told me to consider (in working hours) 1 week = 2400 minutes.
I have to calculate the average arrival rate of the machine and the average service time of the machine.
Average arrival rate of the machine = 50 pieces per week + 100 pieces per week = 150 pieces per week, this is simple since each piece counts as an arrival (they're all equal)
I'm confused with the Average service time per piece of the machine...
the machine can serve 2400/20 type 1 pieces per week = 120 and 2400 / 8 type 2 pieces per week = 300
so average_service_rate = (120*50 + 300*100) / 150 = 240, but this is wrong according to my solution (which is 200)...
if I use service times it works: time per each type 1 piece: 20 min time per each type 2 piece: 8 min average_time_per_piece = (20*50 + 8*100)/150 = 12 min, i.e. 12/2400 week so 1/averaget_time_per_piece = average_service_rate = 2400/12 = 200. And this is the right value.
My question is: why my first approach with the average frequency didn't work? What's wrong with it?