A Note on the Linear Programming Sensitivity Analysis of Specification Constraints in Blending Problems

In blending problems there are typically specification constraints that limit the content of various properties of the blend that it acquires from the ingredients to certain maximum or minimum percentages of the total blend. For sake of linearity, these constraints are commonly included in the problem in a way that precludes direct sensitivity analysis with respect to changes in these percentages. This note shows that the sensitivity analysis with respect to changes in the target specification percentages can be derived from the ordinary sensitivity analysis with minimum additional effort; and that common LP codes can be slightly modified to facilitate sensitivity analysis of blending percentages.