$(15$ points$)$ The two$-$week MPS figures for products A and $B$ are given in the table below.

$\backslash$table$[[$Product$,$Week$],[1,2],[A,200,400],[B,300,100]]$

The total hours to produce one unit of items A and $B$ are $0\mathrm{.}30$ and $0\mathrm{.}20$ hours, respectively. For producing each product, three work centers are used. Each work center is operated $5$ days in a week, $2$ shifts in a day, and $8$ hours in a shift. Utilization and efficiency in the work centers and the bill of labor for the products A and $B$ in three work centers are given in the table below.

$\backslash$table$[[$Work Center,Utilization $(\%),$Efficiency $(\%),$Time $($hours$/$unit$)],[A,B$