// v2-page.jsx — Full intro page in V2 "pantry stickers" style. // Composes: hero → essay + scenarios → 2D LP graph → mini tool → examples. function V2Intro() { const grains = evaluate(SCENARIOS.justGrains, 'fao'); const beans = evaluate(SCENARIOS.justBeans, 'fao'); const combo = evaluate(SCENARIOS.beansRice, 'fao'); const opt = evaluate(SCENARIOS.optimized, 'fao'); const [exampleSeed, setExampleSeed] = React.useState(null); return ( {/* masthead */}
A
Optimize Amino
Essay № 01 · the pantry notebook
{/* HERO */}

Nine acids,
one grocery list.

Picking vegan meals that cover every essential amino acid, at the lowest price — solved as a linear program, told as a story, with a solver you can run on your own pantry.
15 min read · runnable cells · receipts print at the end
{/* decorative stickers */}
{/* §1 */}

Your nutrition label treats protein as a lump. Your body does not. It tears whatever you ate back down into twenty amino acids, nine of which it cannot make itself. A meal is only as useful as its scarcest essential amino acid — Liebig’s law of the minimum, borrowed from agronomy.

So “did I get enough protein?” is really nine questions stacked on top of each other. That’s why beans-and-rice works — and why it only almost works.
{EAA.map(a => (
{a.key}  {a.full} {PATTERNS.fao.v[a.key]}
))}
FAO/WHO/UNU 2007 adult maintenance pattern. Multiply each by 52 g protein to get daily targets in mg.
{/* §2 scenarios */}

Four day-long meal plans, one question asked of each: does this cover all nine? We start at the corners — grains alone, legumes alone — to see the hole each leaves. Then the famous pair. Then the optimum.

 {/* 2a — grains */} {/* 2b — legumes */} {/* 2c — beans & rice */} {/* 2d — optimum */}
{/* §3 — 2D LP graph */}

Dial the pantry down to two foods — just grain and legume, two amino acid floors (lysine, methionine+cys) and a budget ceiling — and the whole LP fits on a page. Every axis is a food. Every line is a constraint. The shaded wedge is the feasible region: meals that satisfy everything at once. The dotted point is the cheapest one.
← every meal
is a point optimum:
on the budget line
Add a third food and this becomes a polyhedron in 3D. Add a fourth, and we can no longer draw it — but the solver still finds the vertex with minimum cost in milliseconds.
{/* §4 — the LP written out */}

Let xi be grams of food i. The solver picks{' '} x to minimise grocery cost while covering every amino acid.
minimize   Σi ci · xi   // grocery cost
subject to
Σi aij xi ≥ bj   ∀ j ∈ {'{'}His, Ile, Leu, Lys, Met, Phe, Thr, Trp, Val{'}'}
xi ≥ 0   ∀ i ∈ pantry
+ optional ratio & bound constraints (Lys:Arg, LNAA, BCAA…)
{/* §5 — mini tool */}

Pick a reference pattern. Tick the pantry items you have on hand. Add any fixed foods (today’s fruit, condiments, a smoothie). Press run — a receipt prints with the optimum.
{/* §6 — examples */}

Six worked examples. Click one to load its pantry and constraints into the tool above, then press run to see what the solver does.
{EXAMPLES.map((ex, i) => ( ))}
{/* footer / link to tool page */}
Tool page
Skip the essay. Just solve.
→
{/* anchor for the examples to scroll to */}
); } // ───────────────────────────────────────────────────────────── // One scenario row: meal chips + amino bars + takeaway note // ───────────────────────────────────────────────────────────── function ScenarioRow({ num, title, meal, tint, tape, result, note, takeaway }) { return (
§ {num}

{title}

${result.cost.toFixed(2)} · {result.protein.toFixed(1)} g protein
{/* left: meal chips + takeaway */}
today's plate
{Object.entries(meal).map(([id, g]) => { const f = FOODS.find(x => x.id === id); return f ? : null; })}
{note}
{takeaway}
{/* right: amino bars */}
amino coverage vs. target
); } Object.assign(window, { V2Intro, ScenarioRow });