APPLYING THE SIMPLEX METHOD TO SOLVE A LINEAR PROGRAMMING PROBLEM Is the problem in standard form? NO STOP: The basic simplex method is not applicable. YES Form the initial simplex tableau Are there negative indicators in the last row to the left of the P column? NO STOP: You have the optimal solution. Set the nonbasic variables =0 and assign the basic variables the values in the last column. YES Choose the pivot column. (If no positive elements in the pivot column above the dashed line, the L.P.P. has no optimal solution.) Choose the pivot row. Pivot about the pivot entry. Inspect the simplex tableau you obtain. SIDE NOTES: **STANDARD FORM: 3 conditions must be met: (1) Objective function is to be maximized, (2) Variables are all nonnegative, and (3) the other constraints must be of the form (linear polynomial) a where a is a positive number or zero. **PIVOT COLUMN: The column that has the most negative entry in the last row. **PIVOT ROW: For each row, except the last one, with a positive entry in the pivot column, compute the ratio of the number in the last column to the number in the pivot column. The pivot row is the row with the smallest nonnegative ratio. If denominator is 0, no ratio is formed. If there are 2 or more rows that have the same ratio, any of these rows may be selected. **PIVOTING: Using row operations, change the pivot entry to 1 and all other entries in the pivot column to 0.