Graphing the Feasible Space

In Figure 9.5, the graph of the constraint equation for input A, 4QX + 2QY = 32, indicates the maximum quantities of X and Y that can be produced given the limitation on the availability of input A. A maximum of 16 units of Y can be produced if no X is manufactured; 8 units of X can be produced if the output of Y is zero. Any point along the line connecting these two outputs represents the maximum combination of X and Y that can be produced with no more than 32 units of A.

This constraint equation divides the XY plane into two half spaces. Every point lying on the line or to the left of the line satisfies the constraint expressed by the equation 4QX + 2QY < 32; every point to the right of the line violates that expression. Only points on the constraint line or to the left of it are in the feasible space. The shaded area of Figure 9.5 represents the feasible area limited by the constraint on input A.

In Figure 9.6, the feasible space is limited further by adding constraints for inputs B and C. The constraint on input B is expressed as QX + QY = 10. If no Y is produced, a maximum of 10 units of X can be produced; if output of X is zero, 10 units of Y can be manufactured. All combinations of X and Y lying on or to the left of the line connecting these two points are feasible with respect to utilization of input B.

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