Green Corporation, located in Guelph, is a world-class designer and diversified manufacturer of precision metallic components and systems for the automotive industry, energy and mobile industrial markets. The company is a leading edge supplier of engine, transmission, driveline, modules & systems and mobile aerial work platforms. Green wants to determine the production order quantity for its engines. Annual demand for engine is 160,000 units. Setting up equipment costs $2.75. The holding cost is $1.50 per engine per year. The company operates its production facility 300 days per year. Green has a capability of producing 850 engines per day. The cost of each engine is $3000. 

Suppose the company retains a service crew to repair machine breakdowns that occuron an average of four per hour, according to a Poisson distribution. The crew can service an average offiveper hour, following approximately the exponential distribution in service times. The salary and benefits for a crew would be $25 per hour. The company operates 8 hours each day. It has been estimated that the waiting time cost is $25 per hour in the line, in terms lost productivity.

a) What is the utilization rate of this service system?

b) What is the average downtime for a machine that is broken?

c) How many machines are waiting to be serviced at any given time?

d) What is the probability that zero machine is in the system?

e) What is the average time a machine spends in the queue?

f) What is the total daily waiting cost based on time in the queue?

g) What is the total daily service cost?

h) What is the total daily cost of the queuing system?