Consider the linear program min -y1 + 5y2 s.t. -y1 + y2 3 y2 2 y2 y1 y1, y2 0 at

Consider the linear program min -y1 + 5y2 s.t. -y1 + y2 … 3 y2 Ú 2 y2 Ú y1 y1, y2 Ú 0 at current solution y112 = 10, 32.

(a) List the condition for a direction y to be improving at y112.

(b) Show that direction y = 11, -12 satisfies your condition of part (a).

(c) Determine which constraints are active at y112.

(d) List and justify all conditions for any direction y to be feasible at point y112.

(e) Show that direction y = 11, -12 satisfies your conditions of part (d), determine the maximum feasible step l in that direction from y112, an compute the next solution point y122.

(f) Draw a 2-dimensional plot of the feasible space for this LP including contours of its objective. Then show how y = 11, -12 improves the objective, identify y112, and demonstrate how the same y preserves all constraints until it encounters an inactive one at the l of part

(e) to produce y122.