It is required to produce 42000 units of good quality in the coming 7 weeks. Each unit requires 8 minutes to be processed. The factory operates three shifts a day, 8 hours each shift, 6 days a week with the following capacity information

Shift MUR LE

1 96% 104%

2 93% 95%

3 88% 90%

The average scrap rate is 1%, How many machines should be available? JUSTIFY YOUR ANSWER.

MUR: machine utilization rate LE: labor efficiency