You operate a carwash with one machine. When you charge $10 per wash you expect to have 20,000 customers per year. For every 10c reduction in price you expect to add 250 customers per year. Your fixed cost is $100,000 per year and your variable cost is negligible. Your carwash is open 300 days a year 10 hours per day. It takes about 5 minutes to wash a car. Assume Poisson arrival and exponential service time. You consider pricing your car wash between $8 and $10 in 10c increments in order to maximize profit. Note that the arrival rate depends on the price you charge. 1. What price should you charge to maximize your profit disregarding customers’ waiting time in line?
2. Suppose you lose 2c per minute of waiting in line per customer in good will (future business). How much should you charge to maximize profit? What will be your profit? How many customers will you serve? You must use data table for this question.
3. Find the best price by using Solver