A toy company currently operates for $40$ hours per week and sells and average of $6,000$ toys per week. The manufacturing process consist of three basic operations: molding,

painting and finishing $($performed in that order$).$ Changing over between different versions of toys requires setup time at painting and finishing. The table below lists the setup times

for a batch and the processing times for each unit at each step. There is unlimited buffer space between these steps. Assume that:

Setups need to be completed first

A setup can only start once the batch has arrived at the resource

All flow units of a batch need to be processed at the resource before any of the units of the batch can be moved to the next resource.

What is the process capacity in units per hour with a batch size of $300$ toys? $($report your answer as toys$/$per hour as an integer$)$

What batch size would minimize inventory without decreasing the process capacity?$($report your answer as an integer$)$

What batch size would minimize inventory without decreasing the current flow rate? $($report your answer as an integer$)$