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. From 8:00AM to 10:00AM, new customers arrive at the rate of 5 per minute. After 10:00AM, the rate reduces to 2 per minute. The store admits customers at the rate of 4 per minute.
a. Jacob plans to arrive to the store at 9:00AM. How long should he expect to wait?
b. Rachel does not want to wait more than 15 minutes. When should she show up?

Question

Quizplus · Accepted Answer

The Answer is At 8:00Am, 120 customers are waiting
From 8:00 to 10:00AM, line increase by 1 customer per minute
From 10:00 to 12:00PM, line decrease by 2 customers per minute
a. At 9:00 the line is 180. Jacob will wait 180/4 = 45 minutes
b. To wait 15 minutes, the line has to be at most 15*4 = 60. Rachel must show up after 11:30AM

The "Steal a Deal" Gift Shop Specializes in Heavily Discounted