Math Problem Statement
Solve the linear programming problem by the simplex method. Maximize P = x + 4y − 2z subject to 3x + y − z ≤ 52 2x + y − z ≤ 26 −x + y + z ≤ 52 x ≥ 0, y ≥ 0, z ≥ 0 The maximum is P = at (x, y, z) =
.
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Programming
Optimization
Simplex Method
Formulas
Objective Function: P = x + 4y - 2z
Constraints: 3x + y - z ≤ 52, 2x + y - z ≤ 26, -x + y + z ≤ 52
Theorems
Fundamental Theorem of Linear Programming
Simplex Algorithm
Suitable Grade Level
Grades 11-12
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