A company manufactures three types of lamps, labeled A$,$ B$,$ and C$.$ Each lamp is processed in two departments, I and II$.$ Total available work$-$hours per day for departments I and II are $407$ and $593,$ respectively. No additional labor is available. Time requirements and profit per unit for each lamp type are shown in the table to the right. The company has assigned you as the accounting member of its profit planning committee to determine the numbers of types of $A,B,$ and $C$ lamps that it should produce in order to maximize its total profit from the sale of lamps. The following questions relate to a linear programming model that your group has developed.

$\backslash$table$[[,$A$,$B$,$C$],[$Work$-$hours in I,$2,3,1],[$Work$-$hours in II$,4,2,3],[$Profit per Unit,$$6,$$$5,$$$4$