As Patrick Sportwear Co. completes plans for its new assembly line of Liverpool, it identifies 30 different tasks in the production process. VP of Operations Kevin Keegan now faces the job of balancing the line. He lists precedences and provides time estimates for each step based on work-sampling techniques. His goal is to produce 1.000 football shoes per standard 35-hour workweek.

a) Balance this operation using the shortest operation time rule and compute the efficiency of the line. (10%)

b) Explore if this balance could be improved (7%).

c) Discuss if is it possible to improve this balance to 100%? (3%)

\begin{tabular}{|c|c|c|c|c|c|} \hline Task & \begin{tabular}{c} Time \\ (sec) \end{tabular} & \begin{tabular}{c} Immediate \\ Predecessors \end{tabular} & Task & \begin{tabular}{c} Time \\ (sec) \end{tabular} & \begin{tabular}{c} Immediate \\ Predecessors \end{tabular} \\ \hline B1 & 50 & - & E2 & 18 & G5, F3 \\ \hline K4 & 24 & B1 & A4 & 10 & E1 \\ \hline K9 & 27 & B1 & E3 & 109 & F3 \\ \hline J1 & 66 & B1 & D6 & 53 & F4 \\ \hline C2 & 12 & - & D7 & 72 & F9, E2, E3, K9 \\ \hline J2 & 22 & B1 & C1 & 78 & F7, A4 \\ \hline J3 & 3 & C2 & D8 & 78 & E3, D6 \\ \hline D5 & 6 & - & D9 & 37 & D6, A4 \\ \hline G4 & 79 & K4, K9 & C3 & 40 & F9, D7 \\ \hline G5 & 29 & K9, J1 & B3 & 72 & D7, D8, D9, C1 \\ \hline F3 & 32 & J2 & B5 & 108 & C1 \\ \hline F4 & 92 & J2 & A1 & 52 & B5 \\ \hline F7 & 21 & J3 & B7 & 18 & A1, B3, C3 \\ \hline E1 & 20 & C2 & A2 & 72 & B5 \\ \hline F9 & 126 & G4, K4 & A3 & 114 & B7, A1, A2, D5 \\ \hline \end{tabular}