Maria opened her authentic Mexican restaurant MiCazuela in Tucson inthe 1980s. It quickly became popular for the tasty food and use of fresh organicproduce and all-natural meats. Let's suppose that she hired you to run therestaurant temporarily. If you are able to gain herconfidence, she will hireyou permanently. You have definite ideas about increasing theprofitability atMiCazuela. Lately, you have observed a troubling trend in the restaurant.An increasing number of customers are expressing dissatisfaction with the longwait, and you have also observed that some people leave without being served.Your initial analysis of the situation at MiCazuela indicates that one way toimprove customer service is to reduce the waiting time in the restaurant. Youalso realize that by optimizing the process for the peak time in the restaurant,you will be able to increase the profit. Customers arrive in groups that vary insize from one to four. The distribution of the group size (GZ for short) is asfollows:

0.1       n = 1

P(GZ = n) = {             0.5       n = 2

0.15     n = 3

0.25     n = 4

Currently, there are four tables for four and three tables for two patronsin the dining area. As customer groups arrive, they wait to be seated by ahost/hostess. There is space for only 5groups to wait in the lobby of therestaurant. If a group arrives and there are 5 groups already inthe lobby, theywill not wait to be seated and leave immediately. One- or two-customer groupsare directed to tables for two. Three- or four-customer groups are directed totables for four.There are two cooks in the kitchen and two servers. The cooksare paid $100/day, and thewaiters get $60/day. The cost of raw material (vegetables, meat, spices, and other food material)is $1 per customer. The overheadcost of the restaurant (rent, insurance, utilities, and so on) is $300/day. Thebill for each customer varies uniformly from $10 to $16. The restaurant remainsopen seven days a week from 10AM till 10PM. The customer arrival pattern isin Table 1. Thetotal number of customer groups visiting the restaurant eachday varies normally with mean 40and standard deviation 7.

From                To                    Percent

10 A.M.           11 A.M.           5%

11 A.M.           1 P.M.             20%

1 P.M.             5 P.M              20%

5 P.M.             7 P.M. 30%

7 P.M              9 P.M. 15%

9 P.M.             10 P.M.           10%

Table: Customer Arrival Pattern

Processes at the Restaurant:

When a table of the right size becomes available and the host/hostess is free, heor she seats the customer. The server then takes down the group's drink orderand delivers the beveragesordered. The server then gives the customers anopportunity to read the menu. All customers order an appetizer and an entree.The server writes down the customer group's order and deliversthe ticket to thekitchen. Note that the same server who took the drink order will be in chargeof all tasks relating to that particular customer group until the end of service.Cooks prepare the food in the kitchen, and a dedicated food-runner is taskedwith delivering the food from thekitchen to the customer. Customers enjoythe dinner. Some customers like some dessert after their meal (about 30%).The server is tasked with preparing and delivering the desserts (thedesserts aremade early in the day by Maria, all the server needs to do is serve the dessertproperly). At the end of the meal, the server cleans the table and collectspayment from the customers.