Consider the linear programming problem min subject to 4x1+3x2 + x3 2x1 +5x2 x3 5 x...

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Consider the linear programming problem min subject to 4x1+3x2 + x3 2x1 +5x2 x3 5 x + 3x2 + 4x3 - 6 3x + 2x2x3 4 X1, X2, X3 0 = (1) (a) Write out the dual of the linear programming problem. (10 marks) (b) Formulate problem (1) into a maximization problem in the canonical form. You MUST use the matrix notation and specify clearly the matrices and vectors involved in the formulation. (5 marks) (c) Formulate the dual problem into a minimization problem in the standard form. You MUST use the matrix notation and specify clearly the matrices and vectors involved in the formulation. (5 marks) Consider the linear programming problem min subject to 4x1+3x2 + x3 2x1 +5x2 x3 5 x + 3x2 + 4x3 - 6 3x + 2x2x3 4 X1, X2, X3 0 = (1) (a) Write out the dual of the linear programming problem. (10 marks) (b) Formulate problem (1) into a maximization problem in the canonical form. You MUST use the matrix notation and specify clearly the matrices and vectors involved in the formulation. (5 marks) (c) Formulate the dual problem into a minimization problem in the standard form. You MUST use the matrix notation and specify clearly the matrices and vectors involved in the formulation. (5 marks)