Please answer all parts!

Batching Consider the following process: 3 1 2 (Sophia) 4 (Julie, machine 1) (Neha, machine 2) 3 (Julie) (Ben) The setup time and production time per unit of is as follows: Task Setup time Time per unit (in mins) (in mins) 1 0 3 2 40 8 3 0 18 4 0 5 Julie performs tasks 1. She performs task 1 on every unit in a batch. Then, Neha runs a setup on a different machine before performing task 2 on every unit in the batch. After that, either Sophia or Ben performs task 3 on the units. Finally, Julie does task 4. Tasks 3 and 4 are done by the workers only so they do not require any setups. (a) Compute process capacity in units/hour if the batch size is 35 units. (b) What batch size would you recommend for a process manager who wants to maximize flow rate but is also concerned about average flow time, when the demand rate is 6 units per hour? . . when the demand rate is 8 units per hour? (c) Using the current production batch size of 35 parts, how long would it take to produce a batch starting with an empty system (with no setup done)? Assume that all the units in the batch have to stay together (no smaller transfer batches allowed) when transferred to either Sophia or Ben, who then process the entire batch (the batch cannot be divided among the two workers). Also, all the units have to stay together when transferred from either Sophia or Ben to Julie. (d) Using the current production batch size of 35 parts, how long would it take to produce a batch starting with an empty system (with no setup done)? Assume that the units in the batch do not have to stay together; specifically, units are transferred to Sophia or Ben the moment they are done with task 2 and either Sophia or Ben starts processing as early as possible. Assume that either Sophia or Ben processes the entire batch (the batch cannot be divided among the two workers). Similarly, units are transferred to Julie as soon as they are done with task 3 and Julie processes them as early as possible. (e) (Challenging) Suppose the process manager's first objective is to guarantee that a batch can be ready in 5 hours or less. His second concern is flow rate. What batch size would you suggest, given the assumptions in (c)? given the assumptions in (d)