The Schmedley Discount Department Store has approximately 300 customers shopping in its store between 9 A.M. and 5 P.M. upon Saturdays. In deciding how many cash registers to keep open each Saturday, Schmedley's manager suggests two factors: customer waiting time (and the associated waiting cost) and service costs of employing additional checkout clerks. Checkout clerks are paid an average of $8 per hour. When only one is on duty, the waiting time per customer is about 10 minutes (or 1/6 hour); when two clerks are on duty, the average checkout time is 6 minutes per person; 4 minutes when three clerks are working; and 3 minutes when four clerks are on duty.
Schmedley's management has conducted customer satisfaction surveys and has been able to estimate that the store suffers approximately $10 in lost sales and goodwill for every hour of customer time spent waiting in checkout lines. Using the information provided, determine the optimal number of clerks to have on duty each Saturday to minimize the store's total expected cost.