Query Regarding Simplex

Question

Hi,

In the picture given above, both y0 and y1 doesn't satisfy the constraints, Can we pivot on y1 first and then y0? We are free to choose between y0 and y1 to first pivot right?

Comments

I am slightly confused. Initially, all variables are 0. Thus, y2 is within the allowed bounds (-infinity to 3) while y1 (-infinity to 3) is not.

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You are right i mistakenly chose the wrong variable while drawing, however my question remains the same which is that at first step we are allowed to pivot with any variable right?  E.g i could choose between y1 and y0?

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Our online tool would probably pivot y0 with x0. Our exam and exercise questions estimate the effort based on this order. Other orders might produce more or less steps. Not keeping a fixed order might lead to infinite runs.

Answer 1

In general, you cannot use any variable for pivoting, and of course you should only choose those that do not yet fulfill the constraints. If some yi violates the bound, you need to find a non-basic variable xi that can be modified such that yi has a chance to fulfill the constraints. What that means precisely is formulated on slide 64.

After this, the situation changes. Maybe the other constraint is then also fulfilled, you need to evaluate the new situation from a fresh point of view and cannot really make a long-term plan.