“Both graphical and normal simplex methods can be used to solve linear programming that consists of two decision variables.” Based on your understanding, discuss whether the given statement is true by giving justification.
To analyse the given statement we can say that when we have two variables we can solve it with graphical method, but when we have three or more variables we have the option to solve large LP problems using Simplex Method. The simplex system uses a highly efficient approach. It does not determine the value of the objective function at any point; it starts first with a corner of the viability area in which all the key variables are negative. Then the value of the objective function is gradually shifted from the corner point to the corner point. The method moves on to determine the best solution.
In the resolution of an LP problem with one or two decision variables, the graphical approach is constrained. It gives a simple description of the positions and vertical portions of both feasible and non-feasible areas. Visual interpretation of the dilemma leads to a more logical way of thinking. We learnt, for example, that when a linear programme has a non-empty, confined area, the optimal solution is always one of its viable vertices. It is then important to locate all the crossing points, vertices, and then analyse which vertices are the ideal solution across all feasible vertices.
In order to apply the dual simplex method, convert all ≥ constraint to ≤ constraint by multiply -1.
Max Z =x1-2x2
The problem is converted to canonical form by adding slack, surplus and artificial variables as appropiate
After introducing slack variables
Max Z =x1-2x2+0S1+0S2
Here not all Zj-Cj≥0. (BecauseZ1-C1=-1)
Hence, method fails to get optimal basic feasible solution.
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