Your Company produces $5$ varieties of baby diapers. The demand mix for the diaper varieties fluctuates wildly, but total demand tends to stay steady at $5,000$ units per day. You have a single production line with several steps. You run only a single $8-$hour shift each day. The production line, when running, can produce finished units every $3$ seconds. Each time the line switches from one product variety to the next, the line has to be cleaned, recalibrated, and re$-$started. Thus, setup time is counted from when the machine is shut down until the next unit rolls off the line. The setup time is $20$ minutes, independent of the product variety. Further assume that if the end of the workday comes in the middle of a batch, that they can put the machines on standby and just start right back up and finish the batch in the morning.