Three machines $($A$,$ B and C$)$ are needed to process a unit of a product. The product must be processed

by machine A before going to machine B and machine C$.$ There are two machine C$$s in the process. The

figure below shows the sequence.

Machine A has a processing time of $2$ minutes per piece. Machine B has a processing time of $1$ minute

per unit and machine C has a processing time of $3$ minutes per unit. Handling time per move is

equivalent to $1$ minute. Find the appropriate unit load size common to all processes that minimizes total

processing time of $12$ units. Since there are two machine C$$s in the process, the company does not allow

transporting less than three units and the entire $12$ units to every process.