An existing bread factory has the production process shown in the figure below. Manufacturing bread must be processed through each of the three operations $($mix$,$ bake, pack$)$ in sequence. The mixer can mix enough ingredients for $100$ loaves of bread every $15$ minutes, the oven is capable of baking $100$ loaves of bread every $20$ minutes, and the packing machine can handle a batch of $100$ loaves of bread every $12$ minutes.

a$.$ Please draw the process flow chart for the process described above. What is the throughput time for a single loaf of bread at this facility?