Rewrite Linear Programming lecture: SciPy-only + duality#771
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Full rewrite of the Linear Programming lecture addressing the editorial suggestions in #514. - Drop OR-Tools (GLOP) entirely; solve everything with scipy.optimize.linprog (HiGHS), removing the ortools dependency and the dual-solver presentation. - Restructure the flow: pose both examples first (Example 1 solved graphically, motivating the need for a systematic method on the higher-dimensional Example 2), then introduce standard form, then solve both with SciPy. - Add a Duality section: derive the dual of the production problem, state weak/strong duality, interpret the dual variables as shadow prices, and verify the material shadow price by perturbation. - Note why we use real-valued (vs integer) decision variables. - Rewrite both exercise solutions using linprog. All code cells verified to execute via jupytext. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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Closes #514.
Full rewrite of the Linear Programming lecture (
lp_intro), addressing the editorial suggestions in #514.What changed
Tooling
scipy.optimize.linprog(HiGHS), removing theortoolspip installand the parallel two-solver presentation that confused the narrative.Structure / flow
Duality (the main gap in the old lecture)
The Overview always promised a primal/dual pairing, but the dual was never developed. Now it is:
linprogand observe strong duality (both optimal values= 27.5).(0.625, 0.4375)as shadow prices, and verify the material shadow price by perturbation (relaxing the material constraint 30→31 raises revenue by exactly0.625).linprogreports shadow prices directly via.ineqlin.marginals.Other
linprog.Verification
All code cells were executed via
jupytext --to pyand run successfully; every numerical result quoted in the prose matches the solver output (production27.5, investment141018.24, dual27.5/ shadow prices(0.625, 0.4375), exercises23.33and297.5).🤖 Generated with Claude Code