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What Does the Feasible Region in Optimization Mean?

Optimization is about using the resources at your disposal to maximize income or minimize expenses—to produce as optimally as possible. When you run a business, it’s important to ask yourself how much you should produce, and how much raw material you should use, to maximize your income based on the resources you have available. If you find good answers to these questions, your business should do well.

In linear optimization, you draw a bunch of graphs so that they surround an area in the coordinate system. You should mark this area to visualize which points are relevant to the optimization. The bounded area shows you how much you can produce of each of the available resources (in number of units). Special points in this area show which production combinations provide you with the most income. Finding these points and analyzing them is called optimization.

Graphs of linear optimization

Graphs of linear optimization

The optimal point is always along the edges of the area surrounded by the graphs, because that’s where you use up all your resources. The points inside the area represent production combinations that don’t use all your available resources. It goes without saying that the cases where you earn the most occur when you use all your resources, rather than just some of them. You always make more money when you sell your entire stock instead of just a fraction of it. That means the inner points will never give you the greatest income.

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How to Use the Graphical Method for Linear Optimization