Q3 (8 points) Consider a restaurant that operates between 5pm and 3am. The demand rate is variable, and can be described as follows:

Between 5pm and 7pm, the demand rate is 100 customers/hr

Between 7pm and 9pm, the demand rate is 200 customers/hr

Between 9pm and 1am, the demand is constant and equal to 50 customers/hr

After 1am, no new customers arrive

To serve this demand, the restaurant has employees that work on different shifts. The restaurant knows that each employee has a capacity of 50 customers/hour, and suppose that employees work in parallel. In addition, we know that:

Between 5pm and 7pm, there is only one employee working at the restaurant

After 7pm, and until the restaurant closes, there are two employees working in parallel at the restaurant

(a) Plot the evolution of the demand rate and the service rate (or capacity) of the restaurant. (4 points)

(b) Draw the inventory build-up diagram. (4 points)