A company manufactures Products $A,B,$ and C$.$ Each product is processed in three departments: I, II$,$ and III. The total available labor$-$hours per week for Departments I, II$,$ and III are $1080,1200,$ and $960,$ respectively. The time requirements $($in hours per unit$)$ and the profit per unit for each product are as follows.

$\backslash$table$[[,\backslash$table$[[$Product$],[A$