A machine makes two components; call them types A and B. It takes 250 seconds to switch production between the component types. During that time, no production occurs. When in production, each unit of A or B requires 0.5 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 2 seconds, or 30 units per minute. 

a. Suppose the machine rotates between one batch of 1000 units of A and 1000 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? 

b. Suppose the machine rotates between one batch of 1000 units of A and 1000 units of B. What is the utilization of the machine?

c. Suppose the machine rotates between one batch of 1000 units of A and 1000 units of B. What is the average inventory of B components? 

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.