A shipping company operates a docking facility. On average, 3 ships arrive to unload their cargoes per hour. A team of workers unloads each ship. Each team costs $25 / hour. On average, each team can unload 6 ships in 5 hours. The firm pays an hourly charge of $10 per ship for the delay. What is the optimal number of teams to minimize the total hourly cost of the system? What is the approximate optimal total hourly cost of the system? Answer both in order. (Note: We add hourly cost of workers and hourly cost of the delay to obtain the total hourly cost of the system.)

a) 3 teams, about $110

b) 4 teams, about $105

c) 5 teams, about $125

d) 6 teams, about $150

e) No answer above is correct

3 3 3 3 3 3 lambda, Arrival rate mu, Service rate n, Number of servers 1.2 1.2 1.2 1.2 1.2 1.2 1 2 3 4 5 6 0.83 0.63 0.50 0.42 0.04 0.07 0.08 0.08 3.51 0.53 0.03 Utilization PCO), probability{system is empty} Lg, expected queue length L, expected number in system Wq, expected time in queue W, expected total time in system Probability that a customer waits 0.13 2.63 6.01 3.03 2.53 0.18 0.04 1.17 2.00 0.01 0.84 1.01 0.88 0.70 0.32 0.13 0.05