2. Costa Mesa is a hole-in-the-wall taco shop that is operated by two brothers Diego and...

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2. 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, Maradona's 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 10:00am-11:00am Customer Arriving Rate (customers/hour) 15 20 11:00am-12:00pm 12:00pm - 4:00pm 30 25 228224 5 4:00pm - 7:00pm 7:00pm-9:00pm 9:00pm-10:00pm (a) Draw the inventory build-up diagram. Please write the slopes and mark the beginning (ending) times of each line segment. (4.5 points) Hint: Notice that the capacity also changes over time. (b) What is the average number of customers waiting in the queue? (2 points) (c) What is the average waiting time per customer (in minutes)? (2 points) (d) In a day, for how many hours the queue length is equal to or greater than 15 customers? (1.5 points) 2. 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, Maradona's 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 10:00am-11:00am Customer Arriving Rate (customers/hour) 15 20 11:00am-12:00pm 12:00pm - 4:00pm 30 25 228224 5 4:00pm - 7:00pm 7:00pm-9:00pm 9:00pm-10:00pm (a) Draw the inventory build-up diagram. Please write the slopes and mark the beginning (ending) times of each line segment. (4.5 points) Hint: Notice that the capacity also changes over time. (b) What is the average number of customers waiting in the queue? (2 points) (c) What is the average waiting time per customer (in minutes)? (2 points) (d) In a day, for how many hours the queue length is equal to or greater than 15 customers? (1.5 points)