Problem $1(20$ points$)$ An operator assigns tasks to workstations as efficiently as possible and achieve an hourly output of $40$ units. Assume the shop works a $60-$minute hour. Assign the tasks shown in the accompanying precedence diagram $($times are in minutes$)$ to workstations using the following rules: a$.$ In order of greatest positional weight. Tiebreaker: most following tasks. b$.$ What is the efficiency? $0\mathrm{.}60\mathrm{.}514050\mathrm{.}7$ f $0\mathrm{.}5$ d $100\mathrm{.}8$