CIVILEN 3080 Lecture Notes - Lecture 11: Feasible Region
2 May 2016
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For problems with fewer than four decision variables. Can map onto 2d (two variables) or 3d (thee variables) space. Remember: feasible solution satisfy all constraint equations. 6x1 + 4x2 <= 24 x1 + 2x2 <= 6 x2 x1 <= 1 x2 <= 2 x1, x2 >= 0 (raw materials m1) (raw materials m2) (marked limit) (demand limit) Feasible solution must be in the shaded area. Just because the solution is feasible does not mean it is optimal. 1: single feasible solution, no feasible solution. Unique optima only one point in the feasible region that maximizes/minimizes the objective function. Alternate optima orientation of the objective function line relative to the boundaries of the feasible region can result in numerous or infinite numbers of solutions. No feasible solution constraints contradict each other; problem is over constrained. Unbounded under constrained, such that the objective function can continually move through the feasible region that is not fully bounded.
