I have several questions regarding these methods.
Primal Simplex Method
- Does the pivot element always have to be a positive entry in the table?
- Does the RHS always have to be positive in the pivot row?
- What if I have some negative RHS values?
- How does the procedure differ if we are looking for MAX or MIN problem?
Dual Simplex Method
How do I select a pivot row? Do I select whatever negative value on the RHS or the biggest negative in absolute value?
Does the pivot element always have to be a negative entry in the table?
Is it allowed for the element in the row of Z to be both positive or negative, but not 0?
When performing the ratio test, do I only take care of what absolute value is the smallest?
How does the procedure differ if we are looking for MAX or MIN problem?
Example: Maximize w = -10y1 + 10y2 -15y3
y1 y2 y3 s1 s2 s3 w RHS
-1 1 -1 1 0 0 0 -1
-1 1 1 0 1 0 0 3
1 -1 -1 0 0 0 0 -3
-10 10 -15 0 0 0 1 0
Now, I assume I take a row with a RHS of -3 as a pivot row, but how do I choose a pivot column?
The ratios are: (-10/1 = -10); (10/-1 = -10); (-15/-1 = 15); which one do I use?