# Linear programming Convex Polyhedron

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 2 '18 at 10:51
• Thanks if you add an answer i vote you :) – Qwerto Mar 2 '18 at 10:58

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.