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Unformatted text preview: ENGRI 115 Engineering Applications of OR Fall 2007 The Simplex Algorithm Lab 11 Name: Objectives: Practice the simplex algorithm Demonstrate unboundedness Demonstrate the two phases of the simplex algorithm Key Ideas: Objective function, constraints Optimal solution Geometric representation of a problem, corner points Alternative optima Unbounded feasible region Unbounded problem Infeasibility Reading Assignment: Winston 4.1-4.8, 4.13 Part #1 - Geometry and the Simplex Algorithm Recall the glass manufacturers problem from lecture. Here is the original formulation. Draw a graphical representation of the problem below, including the objective function. max 500 x 1 + 450 x 2 6 x 1 + 5 x 2 60 x 1 + 2 x 2 15 x 1 8 x 1 , x 2 x x 1 2 1 1 10 10 1 Now convert the problem into standard form by introducing a variable z for the objective function value and slack variables s 1 , s 2 and s 3 for the constraints (dont forget the non-negativity of the new variables!). How many variables and constraints are there in the problem now? In general, the simplex algorithm works with basic solutions , which means that the variables can be divided into two groups, non-basic and basic variables, where the number of basic variables is exactly the same as the number of constraints. So in our standard formulation non-basic = x 1 , x 2 ; basic = z , s 1 , s 2 , s 3 is a basic solution. Non-basic variables have value 0; values of the basic variables are deduced from the equation system....
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- Spring '05