OPRE $6302$: Homework $3$ Problem description: Consider a sandwich restaurant for which the steps involved in the process of filling a customer's order are as follows. The customer $($say Zoe is her name$)$ enters the restaurant and grabs the sandwich bag corresponding to the type of sandwich she wants $($chicken$,$ seafood, vegetarian, etc.$).$ Using a red marker, she fills out the list of ingredients she wants, which takes exactly $1$ minute. Once she is done, she gives the sandwich bag to Adam $,$ who works at the cash register $.$ Adam gives Zoe an empty cup for her drink and accepts her payment. These two activities take a total of $1$ minute and $15$ seconds. Then Adam puts the sandwich bag on the "order rack" above the counter, which takes $15$ seconds. The order on the sandwich bag is first read by Bob who picks the bread, adds the cheese and the meat then moves the sandwich bag to the left on the order rack $.$ Bob's tasks take $2$ minutes and $30$ seconds per sandwich. After that $,$ the sandwich moves slowly through a toaster oven $($via a conveyor belt$)$ for exactly $60$ seconds and the sandwich bag stays on the order rack during that time. There can be at most $6$ sandwiches simultaneously toasting in the toaster oven at any point in time. Once the sandwich comes out of the toaster oven $,$ Chloe takes it and adds the rest of the ingredients $($mayonnaise $,$ vegetables $,$ spices, etc.$)$ according to the order on the sandwich bag. Then she takes the sandwich bag off the order rack and puts the sandwich in the bag $,$ while yelling "A hot wich for Zoe!" Adding the rest of the ingredients takes Chloe $1$ minute per sandwich $($ putting the sandwich in the bag takes an insignificant amount of time$)$ Immediately after talking to Adam, Zoe fills up her drink at the soda fountain $,$ which takes $30$ seconds $.$ When her sandwich is ready $,$ she picks it up and leaves $.$ Further, we make the following assumptions : The steps and times listed above are the same for all the types of sandwiches that can be ordered and for all customers ; Every customer orders a sandwich and a soda; Picking up the sandwich takes a negligible amount of time; There are exactly $5$ red markers ; At most one customer can fill up their drink at the fountain at any point in time; At most $30$ sandwich bags can be on the order rack at the same time ; The customers immediately leave the restaurant once they pick up their order and the time it