Interpreting Range Information

In linear programming problems, unlike nonlinear problems, the dual values are constant over a range of possible changes in the objective function coefficients and the constraint right hand sides. The Sensitivity Report for linear programming models includes this range information.

A Sensitivity Report for the Product Mix problem when the Solver "engine" is the standard Simplex or the Large-Scale LP Solver is shown below. In addition to the dual values (Reduced Costs for variables, Shadow Prices for constraints), this report provides information about the range over which these values will remain valid.

For each decision variable, the report shows its coefficient in the objective function, and the amount by which this coefficient could be increased or decreased without changing the dual value. In the example below, we'd still build 200 TV sets even if the profitability of TV sets decreased up to $5 per unit. Beyond that point, or if the unit profit of speakers increased by more than $2.50 -- rounded below for display purposes to $3 -- we'd start building speakers.

For each constraint, the report shows the constraint right hand side, and the amount by which the RHS could be increased or decreased without changing the dual value. In this example, we could use up to 50 more electronics units, which we'd use to build more TV sets instead of stereos, increasing our profits by $25 per unit. Beyond 650 units, we would switch to building speakers at an incremental profit of $20 per unit (a new dual value). A value of 1.00E+30 in these reports represents "infinity:" in the example below, we wouldn't build any speakers regardless of how much the profit per speaker were decreased.