The purpose of the Linearity Report is to help you pinpoint nonlinear formulas in your model. The format of the Linearity Report is similar to that of the Answer Report: It lists each decision variable and constraint on a separate row, with its cell reference, a “name” as described for the Answer Report, the cell’s original and final values, and a column containing “Yes” (the objective or constraint is a linear function, or the variable occurs linearly throughout the model) or “No” (the function is nonlinear, or the variable occurs nonlinearly). Since you are normally interested in the nonlinearities, any “No” entries appear in boldface.
If your objective or constraints are computed through a chain of formulas in different cells that ultimately depend on the decision variable cells, you may want to use Excel’s auditing features to trace the dependents of your formula cells and find the point where you’ve introduced a nonlinear dependence. If you multiply or divide two quantities that both depend on decision variables, the result is nonlinear. Excel functions other than SUM, SUMPRODUCT and selected other cases will compute a nonlinear or non-smooth function of the variables. For more information, see the topic Linear Functions.
Once you identify specific formulas that are nonlinear, you should determine whether they are correct for your problem, and decide whether they can be rewritten as linear functions, or whether there is an alternative, linear formulation of your problem. If you can formulate the model as a linear programming problem, you’ll have the benefit of faster and more reliable solutions – especially if you also have integer restrictions on decision variables. Otherwise, you’ll have to select the GRG Nonlinear or Evolutionary Solving method to solve your problem.