Parametric Linear Programming

​
c
1
0
c
2
2
c
3
3
c
4
0
t
-20
optimum
Min
Max
The maximum of the cost function is -34..
The gradient of the cost function is {-1.,0.07}.
o
o
o
o
o
o
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
t
enters the cost function. Vary
t
to see that the vertex or the edge where the optimum is realized changes.

Details

The problem is to optimize (either maximize or minimize)
z=(
c
1
+
c
2
t)x+(
c
3
+
c
4
t)y
on a convex domain that is the convex hull of the points
A
,
B
,
C
,
D
,
E
,
F
.
The solution (the set of points for which
z
is optimized) is either a vertex or an edge; it depends on the parameter
t
and is colored red. We show the domain, the gradient
n
of the cost function, and display the optimal value of the cost function.

References

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

External Links

Linear Programming (Wolfram MathWorld)

Permanent Citation

Bunduchi Ecaterina, Mandric Igor
​
​"Parametric Linear Programming"​
​http://demonstrations.wolfram.com/ParametricLinearProgramming/​
​Wolfram Demonstrations Project​
​Published: November 16, 2010