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In a simplex tableau, before proceeding with the optimization of the objective function, the rule is that the row corresponding to objective function say z, can't have the basic variable's coefficients other than zero.

Also, the occurrence of basic variable in all the constraints in the tableau should exactly 1 for each variable, that is, the basic variables' coefficients would make an identity matrix in the simplex tableau.

I have tried searching but am not able to reason the above out. I tried creating an example myself but got too confused.

Can someone please give an example explaining how, a simplex method would fail if it doesn't follow any of the above 2 rules.

Thanks

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  • $\begingroup$ Sure, every column of a basic variable is zero at the objective function. This is nothing special. It is 1 for the basic variable and 0 elsewhere. Have you ever looked at a simplex tableau? $\endgroup$ – callculus Sep 17 '18 at 17:53

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