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This document provides an overview of solving a linear programming problem using the simplex method. It introduces the initial problem of maximizing an objective function subject to constraints. Slack variables are added to convert inequalities to equalities. There are 10 basic solutions to this problem. The simplex method works by starting at an initial basic feasible solution and traversing the feasible set to adjacent vertices that increase the objective function. Several iterations of the simplex method are worked through as an example, choosing entering and departing variables to move to solutions with higher objective values. The numerical steps of setting up and updating the simplex tableau at each iteration are also demonstrated.















































