industrial engineering

operation menagement question

Question 3 (25 points): Consider a shopping center with a restaurant facility attached to it. Each hour, 100 customers arrive for shopping from outside to the shopping center and 40 customers arrive from outside to the restaurant. Half of the customers after shopping leave the system, however, other half goes to the restaurant. Moreover, 2/3 of the customers that finish eating at the restaurant goes to the shopping center while the remaining leave the system. The service rates are 200 customers/hr. and 150 customers/hr. for the shopping center and the restaurant respectively. If interarrival times and service times are exponential random variables, then a) Draw the above process and find the fraction of the time that both shopping center and the restaurant are idle at the same time, b) Find the expected number of customers at shopping center and the expected number of customers in the restaurant. c) Find the average time a customer spends in the system