A single model assembly line is being planned to produce a consumer appliance at the rate of $90,000$ units$/$year$.$ The line will be operated at $50$ weeks$/$year$,5$ shifts$/$week$,$ and $6$ hours$/$shift$.$ There will be one worker per station. Previous experience suggests that the uptime efficiency for the line will be $100\%$ and there is no repositioning time. The work elements, their times, and precedence constraints are given in the table below.