It can be seen that since all the values in Cj-Ej row are either -ve or zero optimal solution has been reached.

Final solution is xwhere M is a very large ve number.

Key element in Table 5 comes out to be 2 and it is made unity and all other elements in the key coloumn are made zero with the help of row operations and finally we get Table 6.

First key element is made unity by dividing that row by 2.

An extreme point or vertex of this polytope is known as basic feasible solution (BFS).

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It can be shown that for a linear program in standard form, if the objective function has a maximum value on the feasible region, then it has this value on (at least) one of the extreme points.

But if number of variables increase from two, it becomes very difficult to solve the problem by drawing its graph as the problem becomes too complex. But it is not possible to test all the corner points since number of corner points increase manifolds as the number of equations and variables increases. If they are -ve then they must be made ve by multiplying both side by (-1) and sign of inequality would be reversed. Here slack variables s,, s We start with a feasible solution and then move towards optimal solution in next iterations.

Maximum number of these points to be tested could be m n = m 1! Initial feasible solution is preferably chosen to be the origin i.e. in this case x are the non basic variables in the initial solution.

A system of linear inequalities defines a polytope as a feasible region.

The simplex algorithm begins at a starting vertex and moves along the edges of the polytope until it reaches the vertex of the optimal solution.).

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