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 $960,1140,$ and $900,$ 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$]],\backslash$table$[[$Product$],[$B$]],\backslash$table$[[$Product$],[$C$]]],[$Dept$.$ I,$2,1,2],[$Dept$.$ II$,3,1,2],[$Dept$.$ II$,2,2,1],[$Profit$,$$$18,$$$12,$$$15$