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Graphical Solutions

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 x1≥ 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.