The Sensitivity Report provides classical sensitivity analysis information for both linear and nonlinear programming problems, including dual values (in both cases) and range information (for linear problems only). The dual values for (nonbasic) variables are called Reduced Costs in the case of linear programming problems, and Reduced Gradients for nonlinear problems. The dual values for (binding) constraints are called Shadow Prices for linear programming problems, and Lagrange Multipliers for nonlinear problems.
Constraints which are simple upper and lower bounds on the variables, that you enter in the Constraints list box of the Solver Parameters dialog, are handled specially (for efficiency reasons) by both the linear and nonlinear Solver algorithms, and will not appear in the Constraints section of the Sensitivity report. When an upper or lower bound on a variable is binding at the solution, a nonzero Reduced Cost or Reduced Gradient for that variable will appear in the "Adjustable Cells" section of the report; this is normally the same as a Lagrange Multiplier or Shadow Price for the upper or lower bound.
Note: The formatting of cells in the Sensitivity Report is "inherited" from the corresponding cells in the Solver model. This can make a significant difference in how the Reduced Gradient, Lagrange Multiplier, Reduced Cost and Shadow Prices are displayed. In the example Sensitivity Reports to follow, the various cells in the Product Mix model were formatted to display as integers (0 decimal places), so the entries in the report are formatted the same way. If you select the cell displayed as -2 below (the Reduced Gradient for Speakers), you'll see that the actual value is -2.4999... which has been rounded down to -2. Bear this in mind when designing your model and when reading the report. Since the report is a worksheet, you can always change the cell formatting.
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