File:Linear programming polytope.png

Summary[edit]

The area surrounded by the blue line is the feasible region of the linear programming problem ${\displaystyle \min\{300x_{1}+500x_{2}\;|\;x_{1}+2x_{2}\leq 170,\;x_{1}+x_{2}\leq 150;\;x_{1},x_{2}\geq 0\}.}$

The red lines are potential lines of the objective functions, i.e., all points on such a red lines have the same objective value. The optimal value is 49000, and it is attained at the unique optimal solution (130,20).

The .fig source file is available from me upon request.

Licensing[edit]

I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.