Consider the linear constraints -w1 + w2 1 w2 3 w1, w2 0 (a)

Consider the linear constraints

-w1 + w2 … 1 w2 … 3 w1, w2 Ú 0

(a) Sketch the feasible space in a 2-dimensional plot.

(b) Determine geometrically whether each of the following solutions are infeasible, boundary, extreme, and/or interior:

w112 = (2, 3),w122 = 10, 32, w132 = 12, 12, w142 = (3, 3), and w152 = 12, 42.

(c) For those points of part

(b) that are feasible, demonstrate algebraically whether they are boundary or interior.

(d) Determine for each of the points in part

(b) whether a suitable (nonconstant) objective function could make the point optimal or uniquely optimal. Explain.

(e) Determine which of the points correspond to basic solutions, and when they do, identify the defining active constraints.