Math Problem Statement
Maximize p = 10x + 20y + 15z subject to x + 2y + z ≤ 60 2y − z ≥ 15 2x − y + z ≥ 30 x ≥ 0, y ≥ 0, z ≥ 0. p =
(x, y, z) =
use nonstandard simplex method
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Programming
Optimization
Simplex Method
Formulas
Objective function: p = 10x + 20y + 15z
Constraints: x + 2y + z ≤ 60, 2y − z ≥ 15, 2x − y + z ≥ 30
Slack and surplus variables for inequalities
Theorems
Simplex Method for Linear Programming
Feasibility and Boundedness Theorems
Suitable Grade Level
Grades 11-12, College Level
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