Math Problem Statement

Reddy Mikks produces both interior and exterior paints from two raw materials, M1 and M2. Determine the optimal product mix of interior and exterior paints to maximize total daily profit using linear programming methods, Simplex method, and post-optimal analysis.

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Programming
Optimization
Simplex Method
Duality in LP
Post-optimal Analysis

Formulas

Objective function: Maximize Z = 5x1 + 4x2
Subject to: 6x1 + 4x2 ≤ 24 (M1 constraint)
1x1 + 2x2 ≤ 6 (M2 constraint)
Non-negativity: x1, x2 ≥ 0

Theorems

Fundamental Theorem of Linear Programming
Duality Theorem

Suitable Grade Level

University Level