The process consists of three steps. In the first step, each tray is loaded with a packaged snack, a container with fruit, and a packet with plastic utensils. This activity requires one point two $(1\mathrm{.}2)$ minutes per tray. In Step $2,$ trays are shrink$-$wrapped in batches using a machine that requires a setup of $10$ minutes for each batch of $30$ trays. After the setup, it takes $1$ minute to shrink$-$wrap each tray in the batch. Finally, the last step is to place the trays in airplane food carts. In this step, each tray requires $1$ minute of processing $($i$.$e$.,$ it takes $1$ minute to place one tray in the cart$).$ The capacity of each cart is of $28$ food$-$trays. After filling a cart, it takes an average of $7$ minutes to transport the filled cart to the loading truck and setup another empty cart for placing a new set of trays.

What is the processing rate for step $1,$ measured in units per hour?

What is the processing rate for step $2,$ measured in units per hour?

What is the processing rate for step $3,$ measured in units per hour?

What is the processing rate for the system as a whole?

If we increased the batch size at step $2,$ would that increase the capacity of the system as a whole? $($Explain$.)$