Fix simplex.py

[imengus]

Describe your change:

I discovered that the algorithm I used initially gives suboptimal solutions when a pivot on a slack column is required; the algorithm terminates prematurely.

This pull request changes function inputs and doctests to reflect changes made to the steps of the algorithm. Mainly:

• Tableau init takes arg n_art_vars
• special case added in run_simplex docstring

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Documentation change?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".

[imengus]

Having found an error in the course that taught this simplex algorithm, I ask you to review my changes once more, @cclauss

[imengus]

@CaedenPH sorry about the number of commits; I had issues with ruff etc. Could you please check this version?

[imengus]

To clarify, the old version couldn't optimally solve certain problems like the one I inserted on lines 270-286 in a doctest. I only realised this after that version was merged, given that it is a rare case. I adapted the implementation of other courses to fix this issue, but took the opportunity to add more doctests and checks.

[CaedenPH]

Nice change, thanks for adding the extra doctests.

@tianyizheng02 Pinging for review

[tianyizheng02]

Honestly I'm not super familiar with the simplex algorithm, so I can't confirm whether this fixes the implementation—but the code itself looks good to me