Question

Consider a bar that operates between 5 pm and 3am. The demand rate is variable, and can be described as follows: - Between 5pm and 9pm, the demand rate is 100 customershr - Between 9pm and 11pm, the demand rate is 200 customers/hr - Between 11 pm and 1 am, the demand is constant and equal to 50 customershr - After 1am, no new customers arrive To serve this dernand, the bar has bartenders that work on different shifts. The restaurant knows that each bartender has a capacity of 50 customershour, and suppose that the bartenders can serve customers in parallel. In addition, we know that: - Between 5pm and 8pm, there is only one bartender working at the restaurant - After 8pm, and until the bar closes, there are two bartenders working in parallet Answer the following two questions. Plot the evolution of the demand rate and the service rate (or capacity) of the restaurant.

Answer 1

The bar's demand and service rates are plotted as a function of time, with the demand varying throughout the evening and the service rate dependent on the number of bartenders. Initially, there is one bartender, but after 8 pm, two bartenders work simultaneously to meet the demand.

Step-by-step explanation:

To answer the question regarding the bar that operates between 5 pm and 3 am with varying demand rates, we need to plot the demand and service rates over time and determine how many bartenders are needed to meet the demand. The demand rate changes throughout the night, starting at 100 customers per hour from 5 pm to 9 pm, increasing to 200 customers per hour from 9 pm to 11 pm, and then dropping to 50 customers per hour from 11 pm to 1 am. After 1 am, no new customers arrive.

The service rate is based on the capacity of the bartenders, which is 50 customers per hour per bartender. Initially, one bartender works from 5 pm to 8 pm, and starting at 8 pm, two bartenders work in parallel.

The demand and service rates can be plotted on a graph with time on the x-axis and the number of customers per hour on the y-axis. The graph will show the demand rate as a piecewise function that changes at 9 pm and 11 pm, and the service rate as a step function that changes at 8 pm. It's important for the bar to match the service rate with the demand rate as closely as possible to optimize operations and customer satisfaction.