Assume a model appropriate with LP except for following conditions: (Demonstrate how to reformulate these constraints to appropriate a mixed integer programming model) a. Either inequality 1 or inequality 2 must be valid. x1 + x2 + x3 + x4 ? 4 3x1 - x2 - x3 + x4 ? 3 b. At least two of the given four constraints must be valid: 5x1 + 3x2 + 3x3 - x4 ? 10 2x1 + 5x2 - x3 + 3x4 ? 10 -x1 + 3x2 + 5x3 + 3x4 ? 10 3x1 - x2 + 3x3 + 5x4 ? 10
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2. (points: 3 + 3) Suppose that a mathematical model fits linear programming except for the restrictions that 1. At least two of the following three inequalities holds: 56x1 + 17x2 - 3x3 + 16x4 ≤ 42 3x1 - x2 - x3 + x4 ≤ 12 x1 + x2 + x3 + x4 ≤ 15 2. At least two of the following four inequalities hold: 2x1 + 5x2 - x3 + x4 ≤ 30 -x1 + 3x2 + 5x3 + x4 ≤ 40 3x1 - x2 + 3x3 - x4 ≤ 60 16x1 + 7x2 - 4x4 ≤ 25 Show how to reformulate these restrictions to fit an MIP model.
Adi S.
Consider the following LP model Max Z= 3X1+2X2+5X3 s.t. X1+2X2+ X3+X4 =30 3X1 +2X3 +X5 =60 X1+4X2 +X6 =20 X1,X2,X3,X4,X5,X6≥0 Check the optimality and feasibility of the following basic solutions. XB = [X4; X3; X6] B^-1 = [1 -1/2 0; 0 1/2 0; 0 0 1]
Madhur L.
Consider the following mathematical model minimize x1 + 3x2 + f(x3) + g(x4) subject to the following constraints (a) Either x1 + 2x2 + 3x3 >= 6 or 3x2 + 4x3 >= 9. (b) At least two of the following four inequalities hold. 5x1 + 6x3 + x4 >= 9, 3x1 + x2 + 4x3 <= 10, x2 + x3 >= 1, 3x3 >= 5. (c) If x2 != 2, then x1 >= 3. (d) x4 = 0 or 1 or 2. (e) x1, x2 and x3 are integers. (f) xi >= 0, i = 1, 2, 3, 4. where f(x3) = { 8 + 3x3 if x3 > 0; 3 otherwise, and g(x4) = x4^2. Formulate this as an integer programming problem.
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