A factory produces cardboard boxes. The production sequence consists of three operations: $(1)$ cutting, $(2)$ indenting, and $(3)$ printing. There are three machines in the factory, one for each operation. The machines are $100\%$ reliable and operate as follows when operating at $100\%$ utilization: $(1)$ In cutting, large rolls of cardboard are fed into the cutting machine and cut into blanks. Each large roll contains enough material for $4,000$ blanks. Production cycle time $=0\mathrm{.}03$ minute$/$blank during a production run, but it takes $35$ minutes to change rolls between runs. $(2)$ In indenting, indentation lines are pressed into the blanks to allow the blanks to later be bent into boxes. The blanks from the previous cutting operation are divided and consolidated into batches whose starting quantity $=2,000$ blanks. Indenting is performed at $4\mathrm{.}5$ minutes per $100$ blanks. Time to change dies on the indentation machine $=30$min. $(3)$ In printing, the indented blanks are printed with labels for a particular customer. The blanks from the previous indenting operation are divided and consolidated into batches whose starting quantity $=1,000$ blanks. Printing cycle rate $=30$ blanks $\frac{?}{\text{m}\text{i}\text{n}}.$ Between batches, changeover of the printing plates is required, which takes $20$ minutes. In$-$process inventory is allowed to build up between machines $1$ and $2,$ and between machines $2$ and $3,$ so that the machines can operate independently as much as possible. Assume steady state operation, not startup. Based on this data and information, answer the following:

a$)$ Calculate the production rate of every process. $[1548\mathrm{.}4,1000,1125p\frac{c}{h}r$

b$)$ Determine the bottle neck process. $[$process $2]$

c$)$ Calculate the maximum possible output of this factory during a $40-$hour week, in completed blanks$/$week $($completed blanks have been cut, indented, and printed$).[40,000$ blanks$/$wk$]$

d$)$ Calculate the WIP between processes $1-2$ and processes $2-3$ in one hour. $[548\mathrm{.}4,0$ pc$/$hr$]$

e$)$ State two suggestions to improve the production of the factory. $[$any$]$