Linear programming Convex Polyhedron

Question

When we define the contraints for a linear programming problem we get that the domain is a Convex Polyhedron .

But, i think it's possibile to add also an equality contraint, in this way the domain of the linear programming can turn into a line.

Is this possibile ? All the procedures usually used to solve a linear programming are still applicable ?

A line is a convex polyhedron – Christoph Mar 02 '18 at 10:51 — Christoph, Mar 02 '18 at 10:51
Thanks if you add an answer i vote you :) – Qwerto Mar 02 '18 at 10:58 — Qwerto, Mar 02 '18 at 10:58

score 1 · Accepted Answer · answered Mar 02 '18 at 11:04

A line is a convex polyhedron as well, but not of full dimension (except you have only one variable anyway). Note that you also don't need equality constraints to describe a line in more variables, for example in three variables the constraints $x\le y \le z\le x$ describe a line and if you add $x\ge 0$ you get a ray, which is a polyhedron as well.

Linear programming Convex Polyhedron

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