We have a polyhedron $P\subset R^2$ defined by: $P:=\{ x\in R^2$
$4x_1-2x_2 \leq -8$
$−x_2≤2$
$-2x_1-x_2≤-4$
$−2x_1+x_2≤0$
Let X={(2,0)} Y{(1,2)}
a) Find the dimension of the smallest face $F\subset P$ containing X. Is F a vertex, edge or neither
I found the dim(F)=1, Does that mean F is an edge? because to be a vertex it should be dim(F)=2.
b) Show Y is a face of P. Provide an inequality that is valid for P and that induces Y as a face of P and shows that your inequality indeed has these properties
I found: eq(Y)={1,3,4} and dim(Y)=2
f(eq(Y)={$x\in P|$
$4x_1-2x_2 = -8$
$-2x_1-x_2=-4$
$−2x_1+x_2=0$}
Is this correct?
c)Determine the recession cone rec(P) of P. Identify at least one extreme ray of P and show that it indeed is an extreme ray of rec(P)
This one I don't know how to do. If anyone can help with this one it would be very much appreciated
Thanks to anyone, who can help!