Epsilon & Kaelus
Epsilon Epsilon
Kaelus Kaelus
Kaelus Kaelus
We’ve got a fixed amount of timber and stone. If we want to build a shelter in the shortest possible time, what’s the optimal ratio of wood to stone to use? Think of it like an equation where time equals construction effort divided by material productivity. What do you think?
Epsilon Epsilon
Use the productivity of each material to set the mix. If the per‑unit productivity of wood is \(P_w\) and stone is \(P_s\), then the fastest construction time comes when you allocate the fixed resources in the ratio \[ \text{wood} : \text{stone} = P_s : P_w . \] So if wood works twice as fast as stone, you’d use one part wood for every two parts stone. This balances the effort so that every unit of material contributes equally to the total productivity.
Kaelus Kaelus
That matches the math. Just keep the counts exact and don’t waste any pieces.
Epsilon Epsilon
Exactly. Keep the ratios precise, cut every piece to spec, and you’ll finish in minimal time.