An operation is used to machine 10 kinds of parts. The total weekly requirement for all 10 parts is 900. Each part requires 20 seconds machine time. Assume the machine is to be scheduled for no more than 90% of its total available time. A normal workweek is 40 hours/week, but 4 hours a week are reserved for normal machine preventive and repair maintenance. If the setup for each kind of part is 1 hour:
a. What is the maximum number of setups per week?
b. What is the smallest allowable lot size, assuming all batches are the same size?
c. To reduce the lot size in (b) by 50%, what must the setup time be reduced to?