Dual Simplex Method and Primal Simplex Method
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Exercise 4.25 This exercise shows that if we bring the dual problem into standard form and then apply the primal simplex method, the resulting algorithm is not identical to the dual simplex method.
Consider the following standard form problem and its dual.
minimize x1 + x2 maximize p1 + p2
subject to x1 = 1 subject to p1 < 1
x2 =1 p2<1
x1,x2>0
Here, there is only one possible basis and the dual simplex method must terminate Umnediately. Show that if the dual problem is converted into standard form and the primal simplex method is applied to it, one or more changes of basis may be
required.
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