Assignment:
The Golding Discount Department Store has approximately 300 customers shopping in its store between 9am and 5pm on Saturdays. In deciding how many cash registers to keep open each Saturday, Golding's manager considers 2 factors: customer waiting time(and the associated waiting cost) and the service costs of employing additional checkout clerks. Checkout clerks are paid on average of $4 per hour. When only one is on duty, the waiting time per customer is about 10 minutes or 1/6 hour; when 2 clerks are on duty, the average checkout time is 6 minutes per person; 4 minutes when 3 clerks are on duty; and 3 minutes when 4 clerks are on duty.
Golding's management 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. Using the information provided, determine the optimal number of clerks to have on duty each Saturday to minimize the store's expected cost.
Provide complete and step by step solution for the question and show calculations and use formulas.