This Demonstration illustrates the problem of parametric linear programming for the case of two variables. So a linear cost function is optimized on a convex domain determined by linear inequalities. The parameter enters the cost function. Vary to see that the vertex or the edge where the optimum is realized changes.

The problem is to optimize (either maximize or minimize) on a convex domain that is the convex hull of the points , , , , , .

The solution (the set of points for which is optimized) is either a vertex or an edge; it depends on the parameter and is colored red. We show the domain, the gradient of the cost function, and display the optimal value of the cost function.

Reference

[1] M. Sagaidac and V. Ungureanu, Operations Research, Chişinău: CEP USM, 2004 (in Romanian).