Solve the following problem for the optimal number of clerks:
There are approximately 300 customers shopping in Fackert Department Store in Mexico City between 9 a.m. and 5 p.m. on Saturdays. All those entering the store will make purchases. When deciding how many cash registers to keep open each Saturday, owner Susanna Fackert considers 2 factors: customer 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 to checkout per customer is about 10 minutes (or 1/6 of an hour); when 2 clerks are on duty, average waiting time is 6 minutes per person; 4 minutes when 3 clerks are working; 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 in line waiting to checkout. Using the information provided, determine the optimal number of clerks to have on duty each Saturday in order to minimize the store's total expected cost