Blue Insitute, located in Texas a manufactuer of metallic components, and mobile industrial markets. Blue wants to create the waiting line performance for its production process. The company is to hire a tech to do repairs for machines that break down which is on an average of 4/hr, according to the poisson distribution. Th tech will service an average of 5 machines/hr following the exponential distribution in service times. The benefits and salary per a work is $30/hr. The company operates 8 hours a day and is estimated that the waiting for cost is $50/hr in the line in terms of lost productivity. PLEASE ANSWER A-D AND PLEASE SHOW ALL OF YOUR CALCULATIONS STEP-BY-STEP. Thank you!

A) What will be the utilization rate of the service system?

B) what would be the average time a machine is spent in the queue? What is the average downtime for the machine that is broken? How many chanines are waiting to be serviced at any given time?

C) What's the probability that a zero machine will be in the system? What's the probability that there's three or more machines within the system? What is the probability that there are exactly 3 machines in system?

D) Cacluate what the total daily waiting cost based on the time in queue is. Calculate what the total daily service cost would be? Calculate what the total daily cost of the queuing system will be