A manual assembly line is to be designed to make a small toy product. The work elements, their times, and precedence constraints are given in the table below. The workers will work only $1$ shift per day, each shift will last $9$ hours, including $1$ hour for lunch. Local labor laws require that the workers be allowed a $10-$minute break every $1$ work hour. The current work order requires that $300$ toys must be produced per day.

$\backslash$table$[[$Element$,$Time, $T_e(min),$Preceded by$],[1,0\mathrm{.}4,-],[2,0\mathrm{.}7,1],[3,0\mathrm{.}5,1],[4,0\mathrm{.}8,2],[5,1\mathrm{.}0,2,3],[6,0\mathrm{.}2,3],[7,0\mathrm{.}3,4],[8,0\mathrm{.}9,4,9],[9,0\mathrm{.}3,5,6],[10,0\mathrm{.}5,7,8]]$