Thread: Question about Simplex Method

When using the simplex method for maximizing the objective function value, you arrive at an optimal value when all the coefficients in the objective value function are 0 or negative. How is this different when the objective is to minimize? Is the solution optimal when the coefficients are all 0 or positive?

Are there any other differences such as the rules for choosing a pivot column and row when dealing with a min instead of a max?

Originally Posted by CUEngineering

When using the simplex method for maximizing the objective function value, you arrive at an optimal value when all the coefficients in the objective value function are 0 or negative. How is this different when the objective is to minimize? Is the solution optimal when the coefficients are all 0 or positive?

Are there any other differences such as the rules for choosing a pivot column and row when dealing with a min instead of a max?

The easiest way to minimise the quantity M is to maximise the quantity –M. But then you must remember to take the negative of the answer. For example, to minimise the expression 4x+5y, you use the simplex method to maximise –4x–5y. Say that this maximum value turns out to be –17, then the minimum value of the original expression 4x+5y is +17.