Example: A company makes two products $($say$,$ P and Q$)$ using two machines $($say$,$ A and B$).$ Each unit of P that is produced requires $42$ 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 $32$ 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 $$25$ and the profit per unit of $Q$ is $$20.$ 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.

The aim is to formulate the problem of deciding how much of each product to make in the current week as an LP$.$