Math Problem Statement
Solve Linear Programming Problem by big-M method :
Maximise Z=3X_1+2X_2+〖3X〗_3
subjected to constraints
2X_1+X_2+X_3≤2
3X_1+4X_2+2X_3≥8; X_1,X_2,X_3≥0
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Programming
Optimization
Big-M Method
Simplex Method
Formulas
Objective function: Maximize Z = 3X_1 + 2X_2 + 3X_3
Constraints: 2X_1 + X_2 + X_3 ≤ 2; 3X_1 + 4X_2 + 2X_3 ≥ 8
Slack variable: Add S_1 to ≤ constraint
Surplus variable: Subtract S_2 from ≥ constraint
Artificial variable: Add A_1 to handle equality
Theorems
Simplex Method
Big-M Method (penalty-based method for handling artificial variables)
Suitable Grade Level
College Level (Operations Research, Linear Algebra)
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