A machine makes two components; call them types A and $B.$ It takes $350$ 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 $5$ seconds, or $12$ units per minute.

a$.$ Suppose the machine rotates between one batch of $980$ units of A and $980$ 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 $B?$

Capacity

component pairs per minute

b$.$ Suppose the machine rotates between one batch of $980$ units of A and $980$ units of $B.$ What is the utilization of the machine?

Utilization

percent

c$.$ Suppose the machine rotates between one batch of $980$ units of A and $980$ units of $B.$ What is the average inventory of $B$ components?

Average inventory

units

d$.$ 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.