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 $1\mathrm{.}000$ football shoes per standard $35-$hour workweek.

Task Time

$($sec$)$

Immediate

Predecessors

Task Time

$($sec$)$

Immediate

Predecessors

B$150-$ E$218$ G$5,$ F$3$

K$424$ B$1$ A$410$ E$1$

K$927$ B$1$ E$3109$ F$3$

J$166$ B$1$ D$653$ F$4$

C$212-$ D$772$ F$9,$ E$2,$ E$3,$ K$9$

J$222$ B$1$ C$178$ F$7,$ A$4$

J$33$ C$2$ D$878$ E$3,$ D$6$

D$56-$ D$937$ D$6,$ A$4$

G$479$ K$4,$ K$9$ C$340$ F$9,$ D$7$

G$529$ K$9,$ J$1$ B$372$ D$7,$ D$8,$ D$9,$ C$1$

F$332$ J$2$ B$5108$ C$1$

F$492$ J$2$ A$152$ B$5$

F$721$ J$3$ B$718$ A$1,$ B$3,$ C$3$

E$120$ C$2$ A$272$ B$5$

F$9126$ G$4,$ K$4$ A$3114$ B$7,$ A$1,$ A$2,$ D$5$

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 $100\%?(3\%)$