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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 4.14.8, 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 nonnegativity 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, nonbasic and basic variables, where the number of basic variables is exactly the same as the number of constraints. So in our standard formulation nonbasic = x 1 , x 2 ; basic = z , s 1 , s 2 , s 3 is a basic solution. Nonbasic variables have value 0; values of the basic variables are deduced from the equation system....
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 Spring '05
 TROTTER

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