A printed circuit board (PCB) machine installs integrated circuits onto a board. Before starting to produce a board, the PCB machine requires a 20-minute setup. Once in production, the PCB machine requires only 0.15 minute per board. 

a. Currently, the PCB machine produces 500 boards between setups. Given this operating process, what is the capacity of the PCB machine (in boards per minute)? 

b. Currently, the PCB machine produces 500 boards between setups. Given this operating process, what is the utilization of the PCB machine? 

c. Say the PCB machine produces 200 boards between setups and demand is 2 boards per minute. Given this operating process, what is the average inventory of boards at the PCB machine? 

d. Demand for boards occurs at the rate of 2 boards per minute. What is the smallest batch size such that the PCB machine does not constrain the flow rate through the process?