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Rewrite LP lecture: drop OR-Tools, focus on SciPy, add duality (#514)
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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