On average 16 new batches of parts are started through a certain plant each week. average batch quantity is 50 parts that are processed through a sequence of seven machines. setup time per machine per batch averages 4 hours, and average operation time per machine for each part is 12 min. nonoperation time per batch at each machine averages 8 hours. there are 37 machines in the factory. any machine can be set up for any type of batch processed in the plant. the plant operates 40 hours per week. the plant manager complains that almost 65 hours of overtime must be authorized each week to keep up with the production schedule. determine
(a) manufacturing lead time for an average order,
(b) weekly production capacity of the plant if all machines were operated at 100% utilization,
(c) current utilization of the plant, and
(d) average work-in-process (number of parts) in the plant.
(e) why must overtime be authorized to achieve the desired output?