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 in Linear Programming
Formulas
Primal Problem Objective: Max Z = 40x + 60y
Constraints: 3x + 2y ≤ 2000; x + 2y ≤ 1000; x, y ≥ 0
Dual Problem Objective: Min W = 2000u_1 + 1000u_2
Dual Constraints: 3u_1 + u_2 ≥ 40; 2u_1 + 2u_2 ≥ 60; u_1, u_2 ≥ 0
Theorems
Weak Duality Theorem
Strong Duality Theorem
Suitable Grade Level
Grades 11-12
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