A food truck near the business school serves customers during the 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 sizeone unit of stir-fry. The stir-fry cooking works in this manner. First, a batch of orders is cooked in a wok by one person. The cooking depends upon the number of orders in the batch. The time is 2.5 minutes to get the wok hot enough, and the time to cook just one order is 0.5 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. The other process is bagging and accepting payments (done by a separate person), which takes 0.80 minutes per order. Please show work!

1) Calculate the batch size (in orders) that will maximize the overall flow rate (assume there is ample demand)? Do not round the batch size (assume for this calculation that a non-integer batch size is possible).

2) Assume that the average inventory in the process is 1.875 orders of stir fry. What batch size does this imply?

Tell me what number n or is in the equation when you get the answer