Consider A product mix problem with three products, where we aim to maximize the total profit while satisfying certain constraints. Lets assume the following scenario: Products: Product A Product B Product C Given Data: Product A requires $2$ labour hours and $3$ units of raw material per unit produced. Product B requires $2$ labour hours and $2$ units of raw material per unit produced. Product C requires $3$ labour hours and $2$ units of raw material per unit produced. There are $100$ labour hours and $80$ units of raw material available. The profit per unit for Product A is $$30,$ for B is $$20,$ and for C is $$25.$ What is the maximum profit?