A machine makes two components; call them types A and B$.$ It takes $270$ seconds to switch production between the component types. During that time, no production occurs. When in production, each unit of A or B requires $0\mathrm{.}5$ second to be completed. The two components, A and B$,$ are combined in an assembly process to make a final product; call it C$.$ The assembly step can combine the two components into $1$ unit every $4$ seconds, or $15$ units per minute.

Suppose the machine rotates between one batch of $1,080$ units of A and $1,080$ units of B$.$ In that case, what is the capacity of the machine in component pairs per minute, where a component pair is one unit of A and one unit of B$?$

Suppose the machine rotates between one batch of $1,080$ units of A and $1,080$ units of B$.$ What is the utilization of the machine?

Suppose the machine rotates between one batch of $1,080$ units of A and $1,080$ units of B$.$ What is the average inventory of B components?

If the production schedule could be adjusted with the goal of minimizing inventory in the process, how many units of A should be produced before switching to component B$?$ Assume the same number of units of B would be produced as well.