Question: c b d SIMPLEX ALGORITHM 1. Consider the following set of constraints: xy + 2x2 + 2x3 + 4x4 S 40 2x1 - x2 +

SIMPLEX ALGORITHM 1. Consider the following set of constraints: xy + 2x2 + 2x3 + 4x4 S 40 2x1 - x2 + x3 + 2x4 58 4x1 - 2x2 + x3 - XA S 10 X1, X2, X3, X4 20 The following parts are independent (10 points each): (a) Consider the objective function as: Maximize z = 8x2 + 6x2 - 4x3 - 2x4. Write the standard form of problem (b)(ONLY standard form DO NOT solve) and consider Xx as a variable with unrestricted sign. (b) Use the simplex method to solve the problem to: Maximize z = 2x + x2 3x3 + 5x4 (e) Use the simplex method to solve the problem to: Maximize z = 8x1 + 8x2 + 3x3 - 2x (d) Use the simplex method to solve the problem to: Minimize z = 5x2 - 4x2 + 6x3 - 8x4 (Hint: You can multiply the objective function by -1 and maximize)

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