You are considering renting some data processing equipments (which are our servers in our queueing system) that are used to process arriving jobs. Inter arrival-time of jobs is exponentially distributed with a mean of 25 minutes. The service time of one server (one data processing equipment) is exponentially distributed with a mean of 15 minutes. The cost of time spent in the system (the waiting time in the queue + service time) is judged to be 10 TL per minute for each job, and renting cost of one data processing equipment is 15000 TL per month. The system works without any break (i.e., 24 hours per day and 30 days per month).

a) Write Monte Carlo Simulations to obtain the total cost for varying number of servers (rented equipments) and plot the graph about the number of servers vs the total cost. (you can find total cost when the number of servers varies from 1 to 8.).

b) Print the graph and find the optimal value for the number of servers. Furthermore, comment on how total cost changes with the number of servers and why?

c) This time, assume that inter arrival-time of jobs is exponentially distributed with a mean of 16 minutes. Again plot the graph (the number of servers vs the total cost) and find the optimal value for the number of servers. Is it different from the result in a). Why or why not?