Math Problem Statement
Dado el siguiente problema primal, conviértalo en un problema dual y halle el valor de las variables de decisión. MaxZ=40x+60ySujeto a:3x+2y≤2000x+2y≤1000x,y≥0 Nota: En el espacio en blanco escriba la solución separada de la letra "y". Ejemplo: 7 y 3 No de finalice con punto, si considera que la solución son tres números sepárelos con una coma y finalice con una "y". Ejemplo: 1, 2 y 3
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Programming
Duality Theory
Optimization
Formulas
Primal: Maximize Z = 40x + 60y
Constraints: 3x + 2y ≤ 200, x + 2y ≤ 100, x, y ≥ 0
Dual Objective: Minimize W = 200u1 + 100u2
Dual Constraints: 3u1 + u2 ≥ 40, 2u1 + 2u2 ≥ 60, u1, u2 ≥ 0
Theorems
Weak Duality Theorem
Strong Duality Theorem
Suitable Grade Level
Undergraduate
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