Apply the simplex method to the next LP relaxation problem to get the optimal solution, provide the steps to get the values of the variables.  

 

 

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Maximize Z=4x12x2 + 7x3 - X4, subject to and X1 x1 + x2 6x1 -X1 - 5x2 +5x3 10 - X3 1 0 - 2x4 3 3 + 2x3 x; 0, for j = 1, 2, 3, 4 x; is an integer, for j = 1, 2, 3. Maximize Z=4x12x2 + 7x3 - X4, subject to and X1 x1 + x2 6x1 -X1 - 5x2 +5x3 10 - X3 1 0 - 2x4 3 3 + 2x3 x; 0, for j = 1, 2, 3, 4 x; is an integer, for j = 1, 2, 3.