7. Linear Programming
Linear programming is a mathematical optimization technique that deals with maximizing or minimizing a linear function subject to linear constraints. The chapter covers the formulation of linear programming problems through practical examples, particularly in the context of maximizing profit from product sales with various constraints. It also explains the geometric interpretation of feasible regions and solutions through vertices.
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What we have learnt
- Linear programming is used to optimize a linear objective function subject to linear constraints.
- The optimal solution for a linear programming problem lies at one of the vertices of the feasible region.
- Complex real-world problems can be formulated into linear programming problems to find optimal solutions.
Key Concepts
- -- Linear Programming
- A mathematical method for determining a way to achieve the best outcome in a given mathematical model, usually involving maximizing or minimizing a linear function.
- -- Feasible Region
- The set of all possible points that satisfy the problem's constraints, graphically represented in optimization problems.
- -- Simplex Algorithm
- An algorithm for solving linear programming problems by iterating through the vertices of the feasible region to find optimal solutions.
- -- Vertices
- Points in the feasible region where constraints intersect, which are candidates for the optimal solution.
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