**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 x_{1}represent the number of units produced of product A and x_{2}represent the number of units produced of B.

then the restriction is represented by

4 x_{1}+ 2 x_{2} ≤60

The problem also implies that x_{1≥} 0 and x_{2} ≥0

In equation 4x_{1}+ 2 x_{2}= 60

We can put different values of one variable to get the value of the other variables i.e., x_{1}= 0, x_{2}= 30 and x_{2}= 0, x_{1}= 15. Hence point A is (x_{1}= 0, x_{2}= 15) and Point B is (x_{1}= 15, x_{2}= 0). This is shown graphically here.

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

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