solve Q2 and c,d from Q1 please

1. Consider the following set of constraints: X1 + 2x2 + 2x3 + 4x4 S 40 2x1 - x2 + x3 + 2x4 S 8 4x1 - 2x2 + x3 - X S10 X1, X2, X3, X4 20 The following parts are independent (10 points each): (a) Consider the objective function as: Maximize z = 8x1 + 6x2 - 4x3 - 2x4. Write the standard form of problem (b) (ONLY standard form DO NOT solve) and consider X, as a variable with unrestricted (b) Use the simplex method to solve the problem to: Maximize z = 2x2 + x2-3x3 + 5x4 (C) Use the simplex method to solve the problem to: Maximize z = 8x2 + 8x2 + 3x3 - 2x4 (d) Use the simplex method to solve the problem to: Minimize z = 5x2 - 4x2 + 6x3 - 8x4 (Hint: Multiply the objective function by -1 and maximize). sign. 2. Consider the following LP (10 points each): Maximize z = 15x1 + 15x2 Subject to 40x1 + 30x2 5 124 -X1 + X2 51 X1