Consider the linear program min -y1 + 5y2 s.t. -y1 + y2 3 y2 2
Question:
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.
Step by Step Answer: