Consider the linear program max 2w1 + 3w2 s.t. 4w1 + 3w2 12 w2 2 w1, w2 0 (a) Solve the problem

Consider the linear program max 2w1 + 3w2 s.t. 4w1 + 3w2 … 12 w2 … 2 w1, w2 Ú 0

(a) Solve the problem graphically.

(b) Determine the direction w of most rapid improvement in the objective function at any solution w.

(c) Explain why the direction of part

(b) is feasible at any interior point solution to the model.

(d) Show that w102 = 11, 12 is an interior point solution.

(e) Determine the maximum step lmax from the point w102 that preserves feasibility in the direction of part (b).

(f) Plot the move of part

(e) and the resulting new point w112 in the graph of part (a).

(g) Explain why it is easier to find a good move direction at w102 than at w112.