Simplex Algorithm

[ftneek]

(11-12-2023 05:11 PM)Albert Chan Wrote:  > m := [[3,2,1,10], [2,5,3,15], [-2,-3,-4,0]]
> time(r := simplex_le(m, -2))                     → 0.0077
> r

\([\displaystyle
\frac{-130}{7},[\frac{15}{7},0,\frac{25}{7},\frac{15}{7},0],... ]\)

(11-11-2023 04:54 AM)ftneek Wrote:  > simplex2([[3,2,1,1,0,10],[2,5,3,0,1,15],[-2,-3,-4,0,0,0],[0,0,0,1,1,0]],{4,5},5,2,0)
[-130/7,[15/7,0,25/7,0,0],...]

Reminder: to avoid incorrect answers for the Dual solution, the 15/7 should really be a 0. This likely just requires either a small modification or new sol() command. The sol command reads a solution for variable I if there there's a 1 and rest 0's in a column. If the column is not in canonical form, the I-th variable is 0.

Specifically, your output has 3 columns in "canonical" form, columns 1,3,4. But column 4 has the 1 in the same position as column 1, thus the answer read for x4 should probably be 0. This issue does not arise when the system is in standard form and the algorithm is run traditionally.