# What Is a Feasible Region?

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A feasible region is an area defined by a set of coordinates that satisfy a system of inequalities. The region satisfies all restrictions imposed by a linear programming scenario. The concept is an optimization technique. For example, a planner can use linear programming to determine the best value obtainable under conditions dictated by several linear equations that relate to a real-life problem.

For example, consider limitations imposed by available production materials and labor and determine the optimal production levels for maximum profits under those conditions. To solve the problem mathematically, a planner first graphs the inequalities that define the production constraints and forms a feasibility region on the x, y-plane. He then pinpoints the coordinates of the corners of the region, such as the coordinates of the intersection points between any two sets of lines.

Applying these coordinates in a given optimization formula can help reveal the highest or lowest possible value; with linear programming theory, optimal conditions must occur at one of the coordinates of the feasible region. To maximize the optimization formula P(x, y) = 3x + 5y, draw the lines of the inequalities on a graph defining the feasible region: x + y 10; x + y 5; y - x 3 and y - x -4.

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