1. Show that the following mathematical program x₁ + x2 subject to min{2x1,3x₂} < x1 - x₂ + 1 and 0 x1, x2 < 1 max 1,22 ER can be cast as a mixed-integer linear program (where R denotes the set of real numbers). (1)
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- Solve the following Integer Programming problem Maximize z = 2x1 + 3x2 subject to 5x1 + 7x2 \leq35 4x1 + 9x2 \leq36 x1, x2 \geq 0 and integerConsider the following linear programming problem Minimize Z=5X1+6X2+3X3 Subject to 5x1+5x2+3x3>=50 x1+x2-x3=20 7X1+6X2-9X3>=30 5x1+5x2+5x3>=35 2x1+4x2-15x3>=10 12x1+10x2>=90 x2-10x3>=20 X1, X2, X3 >=0 In an Excel workbook, solve the problem by using the Solver. Generate the Solver sensitivity and answer reports. In this Word document, write the mathematical formulation of the dual problem. Generate a sensitivity report of the dual problem. Solve the dual problem in another sheet of the same Excel file. In this Word document, describe whether the solution of the dual problem offers a computational advantage and explain why. Submit the Excel workbook as a separate attachment.Consider the following integer linear programming problem Max Z = 3x1 + 2x2 Subject to: 3x1 + 5x2 ≤ 30 4x1 + 2x2 ≤ 28 x1 ≤ 8 x1 , x2 ≥ 0 and integer The solution to the Linear programming relaxation is: x1 = 5.714, x2 = 2.571. What is the optimal solution to the integer linear programming problem?