a$)$ What are the differences between capacity, design capacity, effective capacity, and utilization.$$

b$)$ A manufacturing company operates a production line to assemble electronic devices. The production line runs for $8$ hours a day, $5$ days a week. The setup time for each product variant is $30$ minutes, and the average run time to produce one unit is $5$ minutes. The company aims to produce $400$ units per day to meet demand. Calculate the cycle time, throughput rate, efficiency, and utilization of the production line.$$