3-12 Consider the linear program -y + 5y2 -1 + y 3 1/2 = 2 min s.t. Y/2 = 1 Y, y2 = 0 at current solution y() = (0,3). (a) List the condition for a direction Ay to be improving at y(), (b) Show that direction Ay = (1, -1) satis- fies your condition of part (a). (c) Determine which constraints are active at y(). (d) List and justify all conditions for any di- rection Ay to be feasible at point y() (e) Show that direction Ay = (1, -1) sat- isfies your conditions of part (d), deter- mine the maximum feasible step in that direction from y(), an compute the next solution point y(2) (f) Draw a 2-dimensional plot of the feasible space for this LP including contours of its objective. Then show how Ay = (1, -1) improves the objective, identify y(), and demonstrate how the same Ay preserves all constraints until it encounters an inac- tive one at the A of part (e) to produce y(2).