Question $1$: $[12$pt$]$

A production process at Kenneth Day Manufacturing is shown in the following figure. The drilling operation occurs separately from, and simultaneously with, the sawing and sanding operations. After welding, the product needs to go through exactly one of the three assembly operations $($Hint: the assembly capacity is $\backslash (0\mathrm{.}7\backslash$times $3=2\mathrm{.}1\backslash$mathrm$\{$units$\}/\backslash$mathrm$\{$hr$\}\backslash )).$

a$.$ Which operation is the bottleneck? What is the current capacity of the process? $[5$pt$]$

b$.$ Suppose there is one worker at each operation now. Adding another worker to any operation can double the capacity of that operation. If the operations manager is to hire three additional workers, what positions should be filled? Please present and justify your recommendations? What is the final capacity of this process after adding these three workers? $\backslash (\backslash$quad$[7\backslash$mathrm$\{$pt$\}]\backslash )$