I’ve tried to solve a question in my homework, and I don’t really know what to do. In the problem a polyhedron is given and I need to build the set of constraints that defines this polyhedron.
The faces of the Polyhedron are BCD, BCEO, BDFO, CDFE, EFO.
I never done that or seen an example. I have a "guess", I know that it's 3 dimension so it's probably a linear combination of three vectors, $x_1$, $x_2$, $x_3$ $(x,y,z)$, with other constraints.
\begin{align*} x_1+x_2+x_3&\leq3,\\ x_1&\leq1,\\ x_2&\leq2,\\ x_1,x_2,x_3&\geq0. \end{align*}
Am I right?
After that I need to find the set of vectors C that the face CDFE is the set of optimal solutions for the max problem define by this Polyhedron.
What exactly I need to do in the second part?
Every plane, with equation $ax+by+cz+d=0$, divides all space into two parts (half-spaces) defined by $ax+by+cz+d>0$ and $ax+by+cz+d<0$. Your polyhedron is the intersection of five half-spaces, originating from its five faces.
For instance: faces $BCEO$ and $BDFO$ give two half spaces: $y>0$ and $x>0$. Proceed in the same way to find the other three constraints.