In this case, no maximum of the objective function exists because the region has no boundary for increasing values of x 1 and x 2. The three extreme points (corner points) in the finite plane are: The point (x 1, x 2) must be somewhere in the solution space as shown in the figure by shaded portion. If the feasible region is unbounded then one or more decision variables will increase indefinitely without violating feasibility, and the value of the objective function can be made arbitrarily large. It is a solution whose objective function is infinite. Thus, the problem is infeasible because there is no set of points that satisfy all the three constraints. The region located on the left of ST includes all solutions, which satisfy the second constraint. The region located on the right of PQR includes all solutions, which satisfy the first and the third constraints. For example, let us consider the following linear programming problem. An infeasible LP problem with two decision variables can be identified through its graph. In some cases, there is no feasible solution area, i.e., there are no points that satisfy all constraints of the problem. Thus, every point on the line PQ maximizes the value of the objective function and the problem has multiple solutions. This is indicated by the fact that both the points P with co-ordinates (40, 60) and Q with co-ordinates (60, 50) are on the line x 1 + 2x 2 = 160. All points from P to Q lying on line PQ represent optimal solutions and all these will give the same optimal value (maximum profit) of Rs. In the above figure, there is no unique outer most corner cut by the objective function line.
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