5. [40 points] A restaurant has tracked the average frequency of tables needed for a month for lunch and dinner service. The data is as follows: Tables needed Lunch Avg. Frequency Dinner Avg. Frequency 30 3.6 0 31 4.65 0.31 32 6.4 0.64 33 6.6 0.66 34 3.4 1.7 35 2.45 3.5 36 1.8 7.2 37 1.11 3.25 38 1.52 7.6 39 1.17 3.9 40 0.4 2 A waiter can handle four tables and the restaurant needs one beverage person for each eight tables plus one busboy per twelve tables. To improve customer service the restaurant always rounds up a fractional waiter, beverage, or busboy load. The restaurant wants to simulate the number of tables needed and calculate the staffing required for waiters, busboys, and beverage servers. a. Set up a probability and cumulative probability distribution for the number of tables needed for lunch and dinner services. b. Using Excel random number generator, simulate the table requirement for 2 weeks for lunch and dinner service. Show the table requirement. Determine the staffing required for waiters, busboys, and beverage servers for each day for each service. Show the staffing requirement. Calculate the average staffing requirement per day for waiters, busboys, and beverage servers. Run the simulation for 5 replications with different random numbers. Record the average staffing requirement for each replication. Discuss the variation of staff requirement in each replication. If you were the operations manager of the restaurant, how would you use the simulation results to plan employee scheduling