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Operations analysis

Columbia Pizza and make a pizza in 10 minutes with the one oven that they have. Their late-night business among hungry college students is booming, and they average 5 pizza orders/hour from 9 PM – 11 PM. Between 5 PM and 9 PM, they average 3 pizza orders/hour. Assume that each person orders one pizza, and that people arrive according to a Poisson distribution.

The owner of Columbia Pizza has discovered that if customers have to wait for more than 20 minutes from when they enter the shop to when they receive their pizza, they are likely to go next door to University Falafel, meaning that Columbia Pizza loses a $20 sale.

The owner is thinking of buying a second oven and register (e.g. a second channel). The owner has analyzed that the total cost of operation (the amortized cost of the additional oven and the salary of the staff) would be $75 per night.

Answer each of the questions below. You must show all work. Be sure to highlight your final answer and when asked, please be sure to justify your response.

Calculate the following for the 5-9 shift and the 9-11 shift (20 points)
Average number of customers waiting in line and being served
Average time a customer spends in the store waiting in line and being served (minutes)
Average number of customers waiting in line
Average time a customer spends waiting in line (minutes)
Percent of time Columbia Pizza is serving customers (utilization)
What is the total revenue opportunity for Columbia Pizza, assuming that you can serve all of your customers from 5-9 and 9-11 PM? (5 points)
What is the total revenue opportunity with one oven, given the 20 minute time constraint from entering the shop to receiving their pizza? (5 points)
What is the average daily loss of sales to University Falafel? (5 points)