Math1313-Section3.3-Blank

Math1313-Section3.3-Blank - Section 3.3 Linear Programming...

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Section 3.3 Linear Programming Consider the following figure which is associated with a system of linear inequalities: x y S The set S is called a feasible set. Each point in S is a candidate for the solution of the problem and is called a feasible solution. The point(s) in S that optimizes (maximizes or minimizes) the objective function is called the optimal solution. Theorem 1 (in book) Linear Programming If a linear programming problem has a solution, then it must occur at a vertex, or corner point of the feasible set S associated with the problem. Furthermore, if the objective function P is optimized at two adjacent vertices of S, then it is optimized at every point on the line segment joining these vertices, in which case there are infinitely many solutions to the problem. The Method of Corners 1. Graph the feasible set (graph the system of constraints). 2. Find the coordinates of all corner points (vertices) of the feasible set. 3.
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Math1313-Section3.3-Blank - Section 3.3 Linear Programming...

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