Consider the tiny LP constraint set -w1 + w2 1 w1 + 2w2 1 w1, ww 0 (a) Sketch the feasible set

Consider the tiny LP constraint set

-w1 + w2 … 1 w1 + 2w2 Ú 1 w1, ww Ú 0

(a) Sketch the feasible set of these constraints in a 2-dimensional plot.

(b) Establish that the feasible set is convex.

(c) List all the extreme points of the set.

(d) List all the extreme directions.

(e) Show that each of the following points can be expressed as a convex combination of the extreme points plus a nonnegative combination of the extreme directions:

w(1) = (0, 1), w(2) = (1, 1), w132=10, 1>22.

(f) Is there any feasible point 1w1, w22 for these constraints that cannot be expressed as a convex combination of the extreme points plus a nonnegative combination of the extreme directions? Explain.