Business & Technology

Why a negative coefficient of variable means it is not optimal in Simplex method? Which means why we should make all coefficient non-negative(positive) for optimization of MAX linear programming problem? When we have the following MAX problem. MAX 3x + 5y This can be transformed to the Standard form: z - 3x - 5y As long as we have a negative coefficient in this standard form equation then there is still a way to increase 'z' value by increasing 'x', 'y' as well. However, when having positive one : z + 3x +5y then there is no way to increase 'z' value unless 'x' or 'y' has a negative value. Which is not available by the condition: S.T. x, y >0 Therefore, in order to find the optimum solution of MAX problem, we only need to make sure all coefficients are positive of Objective Function equation.

The Simplex Method - Terminology the simplex method : The method to solve the simplex problem. the optimal solution : The values or methodology of optimal solution slack variables : Functioning as a slack to find the variables in the equations. Simplex tableau : Table summary with variables including a slack the simplex formulation : Formulating the problem into the equations mathmatically. the set of equations : Can be a set of constraints in the context of given problem