For example,
a furniture manufacturer produces wooden tables and chairs. Unit profit for tables is $6, and unit profit for chairs is $8.
To simplify our discussion, let’s assume the only two resources the company uses to produce tables and chairs are wood (board feet) and labor (hours). It takes 30 bf and 5 hours to make a table, and 20 bf and 10 hours to make a chair.
There are 300 bf of wood available and 110 hours of labor available. The company wishes to maximize profit, so profit maximization becomes the objective function.
The resources (wood and labor) are the decision variables. The limitations on resource availability (300 bf of wood and 110 hours of labor) form the constraint set, or operating rules that govern the process. Using LP, management can decide how to allocate the limited resources to maximize profits.