A toy company currently operates for $56$ hours per week and sells and average of $3,476$ 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: