Sum of infeasibilities

Phase 1 minimizes the following linear objective function, the sum of infeasibilities, sinf... 

Select the Show Iteration Results box, click OK in the Solver Options dialog, then click Solve on the Solver Parameter dialog. This causes the simplex solver to stop after each iteration. Because an initial feasible basis is not provided, the simplex method begins with an infeasible solution in phase 1 and proceeds to reduce the sum of infeasibilities sinf in Equation (7.40) as described in Section 7.3. Observe this by selecting Continue after each iteration. The first feasible solution found is shown in Figure 7.6. It has a cost of 3210, with most shipments made from the cheapest source, but with other sources used when the cheapest one runs out of supply. Can you see a way to improve this solution ... 

Iteration Objective Sum of infeasibilities Ratio Max step bound... 

We use a starting point of (0.75, 0). The feasible region is shown in Figure 8.15 as the dashed line segment. At the initial point constraint 1 is strictly satisfied, but constraints 2 and 3 are violated. GRG constructs the phase I objective function as the sum of the absolute values of all constraint violations. For this case the sum of the infeasibilities (sinf) is... 

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