Instructional Design Document Simplex Method - Optimization STAM Interactive Solutions

Demo Outline (For reference) ‏ InteractiveSimulation3 Animated + InteractiveSimplex Method – For Linear Programming 2 Interactive + AnimatedSimplex Method - Explained1 Page TypeTopic NameTopic Number

Simplex Method Optimization Optimization refers to the task of searching for the appropriate point in the domain of a function where the value of this objective function is minimized or maximized. This demo explains the simplest optimization method used for Linear Programming called the Simplex Method.

Simplex Method Optimization Simplex Method - Explained Optimum Value Select the starting point and click START. START Simplex Starting Points

Simplex Method Optimization Simplex Method – For Linear Programming Objective Function: Max Z = 15X1 + 10X2 Constraints: X1 <= 2 X2 <= 3 X1 + X2 <= 4 X1, X2 >= 0 0 X1 <= 2 X2 <= 3 X1 + X2 <= 4 X1, X2 >= 0 Feasible Region Z = 0 Z = 30 Z = 50 Z = 45 Click on the labels for details.

Simplex Method Optimization Simulation Two options for interactivity: Or

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Simplex Method Optimization For Linear Programming, the simplex method is the most efficient method the most effective method the simplest method not an efficient method

Simplex Method Optimization If one constraint is made an equality constraint there are multiple optimal solutions the feasible space is a line a solution is not possible the feasible space is a triangle

Simplex Method Optimization The simplex method can be used for non-linear objective functions with linear constraints linear objective functions with linear constraints linear objective functions with non-linear constraints non-linear objective functions with non-linear constraints

Simplex Method Optimization Using a matrix representation to solve a Linear Programming problem using the simplex method is a convenient way to find the solution the only way to find the optimum particularly well suited for computer programming applicable only if the feasible space is bounded

Simplex Method Optimization For a Linear Programming problem, the simplex method will always locate a local minimum always locate the global minimum locate a global minimum only if the starting point is selected correctly locate the global minimum only if cycling can be avoided