Question: & Systems Engineering Department ISE 303: Operations Research I Term 212 Dated: 15 February 2022 Due Date: 22 February 2022 (Submission on Blackboard) Homework #3

& Systems Engineering Department ISE 303: Operations Research I Term 212 Dated: 15 February 2022 Due Date: 22 February 2022 (Submission on Blackboard) Homework #3 Total Points 50 SIMPLEX ALGORITHM 1. Consider the following set of constraints: *1 + 2x2 + 2xy + 4%, 540 2x1 - x2 + xy + 2x, 58 4x4 - 2xy + xy -- ** $ 10 X1, X3, X5,X420 The following parts are independent (10 points each): (a) Consider the objective function as: Maximize z - 8x + 6xy - 4x3 - 2x 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 + 12 3x3 + 5x (c) Use the simplex method to solve the problem to: Maximize z = 8x + Bxy + 3xy - 2x4 (d) Use the simplex method to solve the problem to: Minimize z = 5x - 4x + 6x - 8x. (Hint: You can multiply the objective function by - I and maximize)

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