Math Problem Statement
- Discrete Optimization using Cutting Plane method Solve the integer programming problem
Maximize: Z = 3x_{1} + x_{2} + 3x_{3} Subject to: - x_{1} + 2x_{2} + x_{3} <= 4 2x_{2} - 3/2 * x_{3} <= 1 x_{1} - 3x_{2} + 2x_{3} <= 3
Where x_{1}, x_{2}, x_{3} >= 0 cutting plane method. and integer. Get the optimal solution as an integer value using Gomory's
Solution
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Math Problem Analysis
Mathematical Concepts
Discrete Optimization
Integer Programming
Linear Programming Relaxation
Gomory's Cutting Plane Method
Formulas
Z = 3x_1 + x_2 + 3x_3
-x_1 + 2x_2 + x_3 <= 4
2x_2 - (3/2) * x_3 <= 1
x_1 - 3x_2 + 2x_3 <= 3
Theorems
Gomory's Fractional Cut
Simplex Method
Suitable Grade Level
Undergraduate (Math or Operations Research)
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