Costa Mesa is a hole-in-the-wall taco shop that is operated by two brothers Diego and Maradona. The shop runs from 10am to 10pm each day. To help the brothers during rush hours, Maradonas 17-year-old son Messi also works in the shop from 2pm to 6pm. Diego, Maradona and Messi have all the same work speed. Such that, individually, they each serve a customer in 6 minutes. The average customer arrival rates are shown in the table below.

Time	Customer arrival rate/(customers/hour)
10:00AM-11:00AM	15
11:00AM-12:00PM	20
12:00PM-4:00PM	30
4:00PM-7:00PM	25
7:00PM-9:00PM	20
9:00PM-10:00PM	5

(a) Draw the inventory build-up diagram. Please write the slopes and mark the beginning (ending) times of each line segment. (12 points)

(b) What is the average number of customers waiting throughout the day?

(c) What is the average waiting time per customer (in minutes)? (5 points) Hint: Consider the changes in capacity when calculating the average throughput rate

(d) In a day, for how many hours the queue length is equal to or greater than 15 customers?