$1.$ A manufacturing company uses two sequential processes to be able to produce the final product. The material must pass through two processes $-$ A and B$.$ Both processes are using machines. Process $\backslash ($ A $\backslash )$ is using one machine and Process B is using two identical machines. The processing time for the machine being used in Process A needs $2$ minutes to process a unit. On the other hand, the machine being used in Process $\backslash ($ B $\backslash )$ needs $3$ minutes to process a unit. The movement of a unit load takes $1$ minute. The management feels that they should not move a single piece nor the entire batch in a single move. Identify the appropriate unit load size that minimizes the processing time of a batch containing $24$ pieces.