Question

Noodles & Co. puts significant importance on minimizing customer waiting times. Trying to achieve the best performance, they hired two chefs to take care of takeaway and dine-in orders separately. Takeaway orders arrive at the rate of one every 5 minutes while dine-in orders arrive at the rate of one every 6 minutes. Each chef can handle the orders at the rate of 15 per hour. All the service times and times between arrivals are exponentially distributed. 1. What is the probability that exactly 4 takeaway orders arrive from 10:00 am to 10:10 am in the morning? (5 marks) 2. What utilization rate for the dine-in chef must be achieved to ensure the probability of having at most 5 dine-in orders in the kitchen is 95%? (8 marks) 3. Would you recommend consolidating the queue for the takeaway orders with the queue for the dine-in orders to increase customer satisfaction? Support your answer with appropriate calculations. (12 marks) Please show your full workings. For any decimals in your workings including final answers, round off to two decimal places, if applicable.

          Noodles & Co. puts significant importance on minimizing customer waiting times. Trying to achieve the best performance, they hired two chefs to take care of takeaway and dine-in orders separately. Takeaway orders arrive at the rate of one every 5 minutes while dine-in orders arrive at the rate of one every 6 minutes. Each chef can handle the orders at the rate of 15 per hour. All the service times and times between arrivals are exponentially distributed.

1. What is the probability that exactly 4 takeaway orders arrive from 10:00 am to 10:10 am in the morning? (5 marks)
2. What utilization rate for the dine-in chef must be achieved to ensure the probability of having at most 5 dine-in orders in the kitchen is 95%? (8 marks)
3. Would you recommend consolidating the queue for the takeaway orders with the queue for the dine-in orders to increase customer satisfaction? Support your answer with appropriate calculations. (12 marks)

Please show your full workings. For any decimals in your workings including final answers, round off to two decimal places, if applicable.

noodles coputs significant importance on minimizing customer waiting timestrying to achieve the best performancethey hired two chefs to take care of takeaway and dine in orders separately ta 68402

Added by Isabel N.

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