We have a supermarket with customers coming with a mean rate of 60 per hour.The boss pays its cashiers $6.00 per hour .The supermarket estimates the goodwill cost of a customer waiting to be served at $5.00 per hour and the goodwill of a customer being served at only $1.50. Customer service times are exponentially distributed with a mean of 3 minutes.
i) Determine the number of cashier person that should be employed to minimize the hourly cost.
ii) If the clients arrival rate increases by 50% and the goodwill cost of a customer waiting to be served increases by $3.00 per hour, determine the number of clerks the boss should employ.
I would really appreciate any help with that problem.