Math Problem Statement

Solve the following linear programming problem. ​Maximize: zequals21xplus11y subject​ to: 3xplus5yless than or equals15 7xplusyless than or equals15 xgreater than or equals​0, ygreater than or equals0 Question content area bottom left Part 1 The maximum value is

Part 2 The maximum occurs at the point

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Solution

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Math Problem Analysis

Mathematical Concepts

Linear Programming
Inequalities
Optimization

Formulas

Objective function: z = 21x + 11y
Constraints: 3x + 5y ≤ 15, 7x + y ≤ 15, x ≥ 0, y ≥ 0

Theorems

Fundamental Theorem of Linear Programming
Feasible Region Theorem

Suitable Grade Level

College or advanced high school (Grades 11-12)

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