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I am working on an optimization problem right now, and I am using the simplex method on the initial tableau. At first, the basic variables are all non-negative and are equal to the slack variables. One of the reducing cost coefficients were positive, so I did a pivot operation.

Right now, none of the reducing cost coefficients are negative, so there is no more steps I can take as far as the simplex method goes. However, two of the four basic variables are negative (if I let the non-basic variables be zero, the right hand side of the equation is a negative constant).

How would I solve such a problem? I know it's a bit hard without seeing numbers, but I this is a problem set I have to turn in and I'd like to know the tecnique behind it.

Thank you

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If your pivot operation took any of the basis variables negative, you mis-calculated the distance you could go in the pivot operation. Did you compare all values of the pivot row ratios and choose the most restrictive constraint to dictate the value of the newly introduced baisis element?

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