2. Please follow these steps to do sensitivity analysis for the LP: max z = 40x; + 100x2 s.t. X: + 2x2 3 40 4x, +3x2 S 120 X4,X, 20 Its optimal solution is x1 = 0.x2 = 20,51 = 0.5, = 60 and z = 2000. The basis for this optimal solution is BV = {xy, 52), NBV = {x1,5), where sz, Szare slack variables for first and second constraint, respectively. 2.1 (2 points) Write the standard form. 2.2 (8 points) Write all related matrices or vectors XBv, XnBy, Cov, Chev, B, N, b and also compute B-1 2.3 (7 points) Let Cz be the coefficient for X2 in the objective function. Currently, C2 = 100. In what range if cz changes (all other parameters stay the same), the current basis remains optimal? 2.4 (4 points) Based on the problem 2.3, ifc, = 90, what are the optimal solution for decision variables, and optimal objective value? 2.5 (6 points) Let b, be the RHS of 1st constraint. Currently, by = 40. In what range if b, changes (all other parameters stay the same), the current basis remains optimal? 2.6 (4 points) What are the shadow prices for the first two constraints of the original LP problem? 2.7 (4 points) Based on the problem 2.5 and the shadow price from problem 2.6, if b. = 60, what are the optimal solution for decision variables and optimal objective value? =