(70 points) BMW produces three different types of wheels - 17-inch, 18-inch, and 19-inch - in its manufacturing facility for the 3 series cars. The production rate is 1000 units per day for each wheel type. However, each time the manufacturing facility switches from producing one wheel type to another, the production should be stopped for one day for configuration of the machinery. Demands for wheels, unit production costs, and fixed configuration costs are as follows: Wheel Demand (units/day) Production cost ($/unit) Configuration cost ($) 17-inch 200 80 8000 18-inch 400 100 8000 19-inch 100 120 10000 The inventory holding cost per unit per year is 20% of the unit production cost for each wheel type. Assume 365 days in a year. BMW wants to implement a rotation cycle policy: the manufacturing facility is set up exactly once for each wheel type in each cycle. (a) How many units of each wheel type should BMW produce each time? How many times should BMW produce a batch of 18-inch wheels each year? (b) What is the optimal total annual cost (inventory holding costs plus production costs plus configuration costs) for these three wheel types? c) What is the maximum inventory level for each wheel type? (d) What percentage of the time is the manufacturing facility busy with producing each wheel type? What percentage of the time is the facility being setup? What percentage of the time is the facility idle? (e) Consider an alternative policy with one setup of 17-inch wheels, two setups of 18- inch wheels, and one setup of 19-inch wheels in each cycle. How many units of each wheel type should BMW produce each time? What is the optimal total annual cost in this case? Make sure the policy is feasible. (70 points) BMW produces three different types of wheels - 17-inch, 18-inch, and 19-inch - in its manufacturing facility for the 3 series cars. The production rate is 1000 units per day for each wheel type. However, each time the manufacturing facility switches from producing one wheel type to another, the production should be stopped for one day for configuration of the machinery. Demands for wheels, unit production costs, and fixed configuration costs are as follows: Wheel Demand (units/day) Production cost ($/unit) Configuration cost ($) 17-inch 200 80 8000 18-inch 400 100 8000 19-inch 100 120 10000 The inventory holding cost per unit per year is 20% of the unit production cost for each wheel type. Assume 365 days in a year. BMW wants to implement a rotation cycle policy: the manufacturing facility is set up exactly once for each wheel type in each cycle. (a) How many units of each wheel type should BMW produce each time? How many times should BMW produce a batch of 18-inch wheels each year? (b) What is the optimal total annual cost (inventory holding costs plus production costs plus configuration costs) for these three wheel types? c) What is the maximum inventory level for each wheel type? (d) What percentage of the time is the manufacturing facility busy with producing each wheel type? What percentage of the time is the facility being setup? What percentage of the time is the facility idle? (e) Consider an alternative policy with one setup of 17-inch wheels, two setups of 18- inch wheels, and one setup of 19-inch wheels in each cycle. How many units of each wheel type should BMW produce each time? What is the optimal total annual cost in this case? Make sure the policy is feasible