The Yum and Yee food truck serves customers during lunch hour by taking orders and making fresh batches of stir fry. Customers have only one choice during the lunch hour, since the objective is to maximize the number of customers served. Assume that each customer places just one lunch order, and all lunch orders are the same size one unit of stir-fry.

The process to produce stir fry has three steps. Ordering and payment are done fully automated via an app (infinite capacity). Then, a batch of orders is cooked in a wok by one worker. The cooking time depends on the number of orders in the batch. The time to cook just one order is 3 minutes. For each additional order in the batch, it takes 0.5 minutes more to cook. Thus, cooking two orders in a batch takes 3.5 minutes, cooking three orders takes 4 minutes, and so on. Then, a different worker bags the food and hands it to the customer, which takes 0.80 minutes per order.

a. If Yum and Yee operate with batch sizes of 8 units, what is their process capacity (in orders per minute)?

b. Calculate the batch size (in orders) that will maximize the overall process flow rate (assume there is sufficient demand to always be capacity constrained)? Round the batch size to two decimal places (i.e., assume for this calculation that a non-integer batch size is possible).