Math Problem Statement

Minimize c = 4x + y + 4z subject to x + y + z ≥ 100 2x + y ≥ 90 y + z ≥ 90 x ≥ 0, y ≥ 0, z ≥ 0.

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Programming
Optimization

Formulas

Objective function: c = 4x + y + 4z
Constraints: x + y + z ≥ 100, 2x + y ≥ 90, y + z ≥ 90, x ≥ 0, y ≥ 0, z ≥ 0
Standard form with slack variables: x + y + z - s1 = 100, 2x + y - s2 = 90, y + z - s3 = 90

Theorems

Simplex Method
Duality in Linear Programming

Suitable Grade Level

College Level