Solve the following linear programs using the simplex method. If the problem is two dimensional, graph the feasible region, and outline the progress of the algorithm. (i) minimize subject to z = -5x17x212x3 + x4 2x1 +3x2+2x3 + x4 38 3x1 + 2x2 + 4x3 - X4 55 X1, X2, X3, X4 0. (ii) (iii) maximize subject to z= 5x + 3.x + 2x3 4x1 + 5x2 + 2x3 + x4 20 3x + 4x2 - x3 + x4 30 X1, X2, X3, X4 20. minimize subject to z= 3x +9x2 5x1 + 2x2 30 -3x1+x2 12 X1, X2 2 0.