lp_intro#

Series: lecture-python-intro
File: lectures/lp_intro.md
Audit date: 2026-08-26
Corpus snapshot: a12d17c0ef
Categories audited: writing, math, code, figures, references, links, admonitions (JAX out of scope)
Overall score: 8.0 / 10
Priority: HIGH

Score breakdown#

Category	Score	One-line note
Writing	3.5/10	`qe-writing-005` ×5; `qe-writing-004` ×3; `qe-writing-001` ×4, +3 more.
Math	6.5/10	`qe-math-002` ×9.
Code	7.5/10	`qe-code-001` ×6.
JAX	out of scope	JAX rules target `lecture-jax`.
Figures	8.5/10	`qe-fig-005` ×1; `qe-fig-008` ×2.
References	10/10	no mechanical violations detected.
Links	10/10	no mechanical violations detected.
Admonitions	10/10	no mechanical violations detected.

None found.

[qe-code-001] (reviewer) — Follow PEP8 unless closer to mathematical notation. Count: 6. Lines: 115, 116, 123, 127, 128, 129. Example: missing space after commas in ax.set_xlim(0,15) and ax.set_ylim(0,10) (115-116), in the polygon vertex list [[0, 0],[0, 6],[2.5, 5],[5, 0]] (123) and in the three iso-revenue plot calls label="...",color='k',linewidth=0.75 (127-129). The column alignment inside the numeric matrix and bounds literals (462, 468-472, 680-682, 741-742) is deliberately matrix-like and is covered by the rule’s own mathematical-notation exception, so it is not counted here.
[qe-math-002] — Use \top for transpose notation. Count: 9. Lines: 287, 305, 380, 562, 564, 598, 637. Example: apostrophe transpose c'.
[qe-writing-005] (reviewer) — Use bold for definitions, italic for emphasis. Count: 5. Lines: 47, 242, 254, 509, 548. Example: the same three terms are bolded as if newly defined each time they recur: dual at 33, again at 47, again at 509, again at 548; standard form at 43, again at 242, again at 254; primal at 31, again at 509 - after the first definition these are emphasis, which the rule assigns to italic.
[qe-writing-008] — Remove excessive whitespace between words. Count: 36. Lines: 27, 31, 70, 80, 160, 166, 168, 170, 172, 176, …. Example: 2 spaces.

[qe-fig-008] — Use lw=2 for line charts. Count: 2. Lines: 118, 119. Example: plot() without lw=.
[qe-writing-001] — Use one sentence per paragraph. Count: 4. Lines: 193, 200, 208, 419. Example: 2 sentences in one paragraph.
[qe-writing-002] (reviewer) — Keep writing clear, concise, and valuable. Count: 4. Lines: 166, 168, 170, 178. Example: the three investment options are stated as 36-43 word run-ons, each packing two or three separate rules into one sentence - the annuity terms plus the must-keep-investing condition (166), the deposit terms plus the borrowing limit plus the repayment terms (168), and the bond availability plus the cap plus the payout (170-172) - and the variable list at 178 is a 32-word sentence that also contains the typo “the amount of put in the annuity”.
[qe-writing-004] — Avoid unnecessary capitalization in narrative text. Count: 3. Lines: 240, 405, 513. Example: mid-sentence ‘Example’.

[qe-fig-005] — Descriptive figure names for cross-referencing. Count: 1. Lines: 109. Example: code-cell figure without mystnb figure metadata.
[qe-writing-007] (reviewer) — Use visual elements to enhance understanding. Count: 1. Lines: 550. Example: the duality section opens with “Let’s develop these ideas using the production problem from Example 1” (513) and the dual it builds at 550-557 has exactly two variables, so it could be drawn with the same feasible-set-plus-iso-line figure the primal gets at 109-138; instead the two shadow prices are only asserted numerically (608) and verified by re-solving (616-624), and the reader never sees the dual feasible region or that the two optimal values meet.

The lecture earns its computational turn: the graphical solution at 109-148 is explicitly shown not to scale (150-154), which is what motivates the standard form and the solver.
The duality section is built from an economic story rather than an algebraic identity - the outside investor pricing material and labor (528-546) - and then the shadow prices are verified numerically by relaxing the material constraint from 30 to 31 and recovering exactly 0.625 (616-624).
Both examples are carried all the way through: stated (86, 223), transformed to standard form (315, 356), and solved with linprog (409, 454), so the reader can see the same problem in three representations.
The note at 628 points out that res_ex1.ineqlin.marginals gives the shadow prices directly, and then explains the sign convention (637-639) rather than leaving the reader to puzzle over the negative numbers.
Every matrix is written with bmatrix (272-280) and the {seealso} at 51 uses an intersphinx {doc} reference to the optimal transport lecture rather than a raw URL.

Replace the nine apostrophe transposes with ^\top - c'x (287, 380, 562), b'y and A'y (564), c'x \le b'y (598), -c'x (637) - the single largest fix in this lecture.
Plot the dual feasible region and iso-cost lines alongside the primal figure so strong duality can be seen rather than only computed.
Break the three investment-option paragraphs at 166-172 into one sentence per rule, and split the four multi-sentence paragraphs at 193, 200, 208 and 419.
Add mystnb: figure: caption/name metadata to the graphical-solution figure at 109 - it is the only figure in the lecture and the prose refers to it as “The following graph” (105) and “The blue region” (140).
Either cite the equation labelled lpproblem (291) somewhere with {eq} or drop the label - as it stands it is the lecture’s only labelled equation and nothing references it.
Replace the 13 uses of \mbox{subject to } with \text{subject to }, set lw=2 on the three constraint lines (118, 119, 132), and strip the 36 runs of double spaces.
Use italic for the recurring emphasis on primal/dual/standard form after their first bolded definition, and fix the index slip at 305 where a free variable is introduced as \(x_i\) and then split into \(x_j^+\) and \(x_j^-\).