Math Problem Statement

Suppose you have a bounded feasible region with corner points (0, 7), (3, 4),(9, 1), and (12, 0). Find the minimum of the objective function C = 3x + 4y on this feasible region, as well as where it occurs. The minimum value of C is ? and occurs at (x, y) = ?.

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Programming
Optimization
Corner Points

Formulas

C = 3x + 4y (Objective Function)
Corner point evaluation for optimization

Theorems

Fundamental Theorem of Linear Programming: The optimal value of the objective function occurs at one of the corner points of the feasible region

Suitable Grade Level

Grades 10-12