Math Problem Statement
Express the problem as a system of equations using slack variables. (Use s1, s2, ... for the slack variables.)
Maximize z = 150x1 + 240x2, subject to 12x1 + 15x2 ≤ 50 8x1 + 22x2 ≤ 65 x1 ≥ 0, x2 ≥ 0.
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Programming
Optimization
Slack Variables
Inequalities
Formulas
Objective Function: z = 150x1 + 240x2
Constraint 1: 12x1 + 15x2 + s1 = 50
Constraint 2: 8x1 + 22x2 + s2 = 65
Theorems
Simplex Method
Feasibility in Linear Programming
Suitable Grade Level
Grades 11-12, Undergraduate
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