Example. A firm manufactures two products. The products must be processed through one department. Product A requires 4 hours per unit and product B requires 2 hours per unit. Total production time available for the coming week is 60, hours. A restriction in planning the production schedule, therefore, is the total hours used in producing the two products cannot exceed. Also, since each variable represents a production quantity, neither variable can be negative. Determine the combination of products A and B that can be produced?

Sol. Let x₁represent the number of units produced of product A and x₂represent the number of units produced of B.

then the restriction is represented by

4 x₁+ 2 x₂ ≤60

The problem also implies that x_1≥ 0 and x₂  ≥0

In equation 4x₁+ 2 x₂= 60

We can put different values of one variable to get the value of the other variables i.e., x₁= 0, x₂= 30 and x₂= 0, x₁= 15. Hence point A is (x₁= 0, x₂= 15) and Point B is (x₁= 15, x₂= 0). This is shown graphically here.

The shaded are represents the combination of products A and B which can be produced.