Math Problem Statement

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Minimize c = x + 2y subject to x + 3y ≥ 22 4x + y ≥ 22 x ≥ 0, y ≥ 0. c =

(x, y)

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Programming
Feasible Region
Optimization

Formulas

Objective function: c = x + 2y
Boundary lines: x + 3y = 22, 4x + y = 22

Theorems

Fundamental Theorem of Linear Programming
Feasible Region and Vertex Theorem

Suitable Grade Level

College level or advanced high school