The Steal a Deal gift shop specializes in heavily discounted merchandise for the

Question

The Steal a Deal gift shop specializes in heavily discounted merchandise for the holiday season.  

The store prices are so appealing that lines of people queue up in the early AM hours in front of the store doors in order to secure a place in the line.

On the morning after Thanksgiving, one of the busiest days of the year, the store opened its doors at 8:00AM. At that time there were 120 customers already waiting in line. The customers leave the line at the rate of 4 per minute. From 8:00AM to 10:00AM, new customers arrive at the rate of 2 per minute.

1) How many people are waiting in line at 9AM?

2) Suppose that there are 151 customers waiting in line at noon, and Jacob arrives at the store at that time. How long should he expect to wait, in minutes?

Explanation / Answer

At 08:00 AM, no. of customers in queue = 120

Arrival rate = 2 per minute

Total new arrivals in 1 hour = 2 * 60 = 120

Departure rate = 4 per minute

Total departures in 1 hour = 4 * 60 = 240

1) In one hour i.e. at 09:00 AM, the total number of people = initial nos. of people in queue + arrivals – departure

At 09:00 AM, total nos. of people = 120 + 120 – 240 = 0

2)

Jacob arrives at noon with 151 people in line.

Departures per minute = 4

All new arrivals will be queued up behind Jacob.

Nos. of minute Jacob has to wait = 151/4 = 37.75 minutes

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