Question II$.$ Problem Statement:

A company makes two products $($say$,$ P and Q$)$ using two machines $($say$,$ A and B$).$ Each unit of P that is produced requires $50$ minutes processing time on machine A and $30$ minutes processing time on machine B$.$ Each unit of Q that is produced requires $24$ minutes processing time on machine A and $33$ minutes processing time on machine B$.$ Machine A is going to be available for $40$ hours and machine B is available for $35$ hours. The profit per unit of P is $$25$ and the profit per unit of Q is $$30.$ Company policy is to determine the production quantity of each product in such a way as to maximize the total profit given that the available resources should not be exceeded.

a$).$ Identify the decision variables.