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Extra resources for Critical Path Analysis and Linear Programming (Texts in Operational Research)
This currently has a profit contribution of £5. 10 it is unlikely to have much, if any, effect on the optimal solution. On the other hand if it changed to, say, £15 then we might expect a change in the optimal mix of production. We are seeking an answer to the question: how much could the profit contribution of B change without affecting the profit maximizing combination of outputs? Recollect the approach we took in the graphical solution. We set an arbitrary level for the objective function in order to be able to draw it on the graph.
It indicates that an organization’s planned activities are not deliverable. Further analysis of the problem can also provide management information on what needs to be done to create a feasible solution. 8 Infeasibility 1200 1400 1600 1800 28 Linear Programming Unbounded problems The second situation occurs when a problem is unbounded. An unbounded problem occurs where the OF can take infinitely large values without violating any of the constraints. An unbounded problem occurs in practice when the problem has not been properly formulated: some critical constraint has been omitted.
We now state that, since D is entering the solution, S2 must leave. At the next stage, therefore, S2 will become non-basic and by definition will take a zero value. Consider what this means. S2 represents the slack resources in terms of constraint 2. If S2 is zero it means that there is no slack – we are using all the resource in production. This must be the case since at Point II this constraint will be binding. So our next solution point will be at Point II. We must now transform the tableau to represent this point since clearly the current values will change.