Q$\mathrm{.}3.$ Two models $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ are to be assembled on a mixed model line. Hourly production rates for the two models are: A$,25$ units$/$hr; and B$,18$ units$/$hr$.$ The work elements, element times, and precedence requirements are given in the table below. Elements $6$ and $8$ are not required for model A $,$ and elements $4$ and $7$ are not required for model B $.$ Assume $\backslash ($ E$=1\mathrm{.}0,$ E$\_\{$r$\}=1\mathrm{.}0\backslash ),$ and $\backslash ($ M$\_\{$i$\}\backslash )\backslash (=1\backslash ).$

$($a$)$ Construct the precedence diagram for each model and for both models combined into one diagram.

$($b$)$ Find the theoretical minimum number of workstations required to achieve the required production rate.

$($c$)$ Use the Kilbridge and Wester method to solve the line balancing problem.

$($d$)$ Determine the balance efficiency for your solution in $($c$).$