1. Consider the following LP: max z=2x+3y s.t. x-2y4 2x + y 18 y10 x, y 0 (a) Suppose we are given the initial feasible solution of x = (x, y) = (0, 0) and the improving direction d=(d, dy)=(2,1). Algebraically determine the maximum step size Amax (b) Using the search direction d, step size Amax and the current solution x, determine the improved solution X and calculate the corresponding change in the objective value. (c) Given the updated point x from part (b), what requirements must a direction d = (dr, dy) satisfy to be a feasible improving direction? (d) Suppose d=(-2, 4), determine the maximum step size Amax when starting at x from part (b). (e) Using the search direction d, step size Amax, and the current solution X, determine the improved solution . (f) Use the General Improving Search Algorithm to show that is optimal.