Just a few questions to make sure I am understanding the simplex method.
First you set up matrice, then you find the column with the largest negative number in bottom row. That is the column you will pivot. So then how do you determine which row is the pivot point? My example gives me its calculation but I do not know where they are getting the numbers from?
Here is my example matrice:
X1 X2 S1 S2 P
1 2 1 0 0 32
3 4 0 1 0 84
-50 -80 0 0 1 0
So my pivot point will be in X2, then what?
duh!!! just figured it out.
dived 32/2 and 84/4, largest is the pivot point.
To determine the row that will be the pivot row, you need to perform a ratio test using the columns of the matrix. Here are the steps to find the pivot row:
1. Select the column that corresponds to the variable you are pivoting on. In your example, you are pivoting on column X2.
2. Examine the numbers in the positive portion of the column. These numbers represent the ratios of the right-hand side coefficients to the coefficients of the pivot column in each equation. In your example, the positive portion of column X2 is {2, 4}.
3. Compute the ratio of each entry in the positive portion of the column to the corresponding entry in the right-hand side column. For example, for the first equation, the ratio would be 32 / 2 = 16. For the second equation, the ratio would be 84 / 4 = 21.
4. Identify the smallest positive ratio. In your example, the smallest positive ratio is 16 from the first equation.
5. The row corresponding to the smallest positive ratio is your pivot row. So, in your example, the pivot row would be the first row because it has the smallest positive ratio.
Once you have identified the pivot row and pivot column, you can use the simplex method to perform the pivot operation and find the new tableau.