Using the simplex method, we know we have an optimal solution when A)all slack variables have a zero value. B)all basic variables are negative. C)all the real variables have a nonzero value. D)the C_j- Z_j row has no positive values.

Question

Quizplus · Accepted Answer

The simplex method works by iterating through a series of pivot operations until the objective function cannot be further improved. At each iteration, a pivot column and row are selected based on certain criteria. The pivot row is determined by finding the variable with the smallest ratio of the constant term to its coefficient in the pivot column among those with positive coefficients. The pivot column is determined by selecting the variable with the most positive coefficient in the objective function row. If the C_j row has no positive values, it means that there is no variable that can be selected as the pivot column, indicating that the current solution is optimal. This is because there are no more positive coefficients in the objective function to increase, and any pivot operation would result in a decrease in the objective function value. Therefore, option D is the correct answer.

Using the Simplex Method, We Know We Have an Optimal