PA $7-2($Algo$)$ A machine makes two components; call...

A machine makes two components; call them types A and B $.$ It takes $510$ 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.

a$.$ Suppose the machine rotates between one batch of $2,040$ units of A and $2,040$ units of B $.$ In that case, what is the capacity of the

machine in component palis per minute, where a component palr is one unit of A and one unit of $B?$

Capacity

component pairs per minute

b$.$ Suppose the machine rotates between one batch of $2,040$ units of A and $2,040$ units of B $.$ What is the utilization of the machine?

c$.$ Suppose the machine rotates between one batch of $2,040$ units of A and $2,040$ 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.