The Yum and Yee food truck near the business school serves customers during lunch hour by taking orders and making fresh batches of stir$-$fry. Customers have only one choice during the lunch hour so that Yum and Yee can 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 stir$-$fry cooking works in this manner. First, one person cooks a batch of orders in a wok. The cooking depends upon the number of orders in the batch. The time to cook just one order is $3\mathrm{.}1$ minutes. For each additional order in the batch, it takes $0\mathrm{.}3$ minute more to cook. Thus, cooking two orders in a batch takes $3\mathrm{.}4$ minutes, cooking three orders takes $3\mathrm{.}7$ minutes, and so on$.$ The other process is bagging and accepting payments $($done by a separate person$),$ which takes $0\mathrm{.}7$ minute per order.

a$.$ What is the setup time of this process?

Note: Do not round intermediate calculations. Round your answer to $1$ decimal place.

Setup time

$3\mathrm{.}8$ minutes

b$.$ If Yum and Yee operates with batch sizes of $6$ units, what is their process capacity $($in orders per minute$)?$

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Process capacity

$4\mathrm{.}60$ orders per minute

c$.$ If Yum and Yee operates with batch sizes of $10$ units, what is the utilization of the wok?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Utilization

$0\mathrm{.}97$ percent

d$.$ Calculate the batch size $($in orders$)$ that maximizes the overall flow rate $($assume there is ample demand$)?$ Do NOT round the batch size $($i$.$e$.,$ assume for this calculation that a noninteger batch size is possible$)$