Parametric Linear Programming

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.

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DETAILS

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).
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