An average of 20 new orders are startcd through a certain factory each month. On average, an order consists of 50 parts to be processed through 10 machines in the factory. The operation time per machine for each part =15min. The nonoperation time per order at each machine averages 8hr, and the required setup time per order =4hr. There are 25 machines in the factory, 80% of which are operational at any time (the other 20% are in repair or maintcnance). The plant operates 160hr/mon. However, the plant manager complains that a total of 100 overtime machine-hours must be authorized each month to keep up with the production schedule. (a) What is the manufacturing lead tume for an average order? (b) What is the plant capacity (on a monthly basis) and why must the overtime be authorized? (c) What is the utilization of the plant according to the definition given in the text? (d) Determine the average level of work-in-process (number of parts-in-process) in the plant