There are approximately 300 customers shopping in Fackert department store in mexico city between 9am and 5pm on Saturdays. When deciding how many cash registers to keep open each saturday, owner Susanna Fackert considers 2 factors; customers waiting time(and the associated waiting cost) and the service costs of employing additional checkout clerks. Checkout clerks are paid an average of $4 per hour. When only 1 is on duty, the waiting time per customer is about 10 minutes (or 1/6 of an hour). When 2 clerks are on duty, average checkout time is 6 minutes per person. when 3 clerks are working, 4 miutes; and 3 minutes with 4 clerks.
Ms. Fackert has conducted customer satisfaction surveys and has been able to estimate that the store suffers approximately $5 in lost sales and goodwill for every hour of customer time spent waiting in checkout lines.
A) The total expected cost with 1 clerk is $
B) The total expected cost with 2 clerks is $
C) The total expected cost with 3 clerks is $
D) The total expected cost with 4 clerks is $
E) The optimal number of clerks to have on duty each saturday in order to minimize the store's total expected cost is ----- clerks?