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GRAPHICAL SOLUTION PROCEDURE 43

Figure 2.4 Feasible Solutions for the Sewing, Finishing, and Inspection and Packaging Constraints,
Represented by the Shaded Regions

D D
1200 1200 (0, 1062)

1000 (0, 720) 1000
Number of Deluxe Bags 800 Constraint Number of Deluxe Bags 800 1S + 0.6667D = 708 Constraint

Sewing
Finishing
600
600
400

200
200 0.5S + 0.833D = 600 Sewing 400 Finishing
(1200, 0) (708, 0)
S S
0 200 400 600 800 1000 1200 1400 0 200 400 600 800 1000 1200 1400
Number of Standard Bags Number of Standard Bags

D
1200

1000
Number of Deluxe Bags 800 (0, 540) Inspection and

Packaging
Constraint
600
(I & P)
400

200 0.1S + 0.25D = 135 I & P
(1350, 0)
S
0 200 400 600 800 1000 1200 1400
Number of Standard Bags

We can do the same for each of the other three constraints. The solutions that are
feasible for each of these constraints are shown in Figure 2.4. We would normally
draw all the constraints on a single graph but here we have drawn them separately to
help you understand the principles more easily.
Four separate graphs now show the feasible solution points for each of the four
constraints. In a linear programming problem, we need to identify the solution
points that satisfy all the constraints simultaneously. To find these solution points,
we can draw all four constraints on one graph and observe the region containing the
points that satisfy all the constraints simultaneously.
The graphs in Figures 2.3 and 2.4 can be superimposed to obtain one graph with
Try Problem 6 to test all four constraints. This combined-constraint graph is shown in Figure 2.5. The
your ability to find the
feasible region given shaded region in this figure includes every solution point that satisfies all the
several constraints. constraints simultaneously. Solutions that satisfy all the constraints are termed

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