Question $4$ a$.$ In a production system with three stages, Stage $1$ can process $200$ units per hour, Stage $2$ can process $150$ units per hour, and Stage $3$ can process $180$ units per hour. If Stage $2$ is upgraded to process $220$ units per hour, what is the new system capacity? Explain your answer. $[3$ marks$]$ b$.$ The efficiency of a factory is $75\%$ and its utilization $50\%.$ If effective capacity is $1000$ find design capacity. $[6$ marks$]$ c$.$ A factory produces $1000$ units a month. If design capacity is $3000$ and efficiency is $50\%$ i$.$ Calculate the utilization rate $[3$ marks$]$ ii$.$ Calculate effective capacity. $[3$ marks$]$ d$.$ An airline company must plan its fleet capacity and long$-$term schedule of aircraft usage. For one flight segment, the average number of customers per day is $70,$ which represents a $65$ percentage utilization rate of the equipment assigned to the flight segment. If demand is expected to increase to $84$ customers for this flight segment in three years, and management requires a capacity cushion of $25$ percent, calculate the following:$-$ MGMT$2026$ Production and Operations Management Semester I $2024-2025$ i$.$ the planned capacity requirement. $[5$ marks$]$ ii$.$ the maximum number of customers the flight segment can accommodate. $[5$ marks$]$