Sentence classification
| Sentence | Label | Note |
|---|---|---|
| "Operates 2 ovens" | Parameter | Both ovens are available. This is not an oven-selection problem. |
| "Plans to bake 300 loaves this week" | Constraint (implicit) | Committed phrasing, so bread = 300 exactly. |
| "May also bake cakes" | Decision | The number of cakes is chosen. |
| "Cakes earn $12, cost $5; bread earns $4, costs $1.50" | Parameters | Net per unit is $7 per cake and $2.50 per loaf. |
| "Each oven runs at most 40 hours" | Parameter (40) and constraint | Oven time used is at most 2 × 40 = 80 hours. |
| "A loaf takes 0.1 oven-hours, a cake 0.4" | Parameters | They set the oven-time usage. |
| "Determine the weekly baking plan" | Objective (implicit) | Revenue and costs are both given, so maximize total profit. |
Formulation
- Decision: c = number of cakes (≥ 0). Integer in practice, though the LP optimum is already whole.
- Fixed by commitment: loaves b = 300.
- Objective: maximize 2.5·b + 7·c, which is profit = revenue − ingredient cost.
- Constraint: 0.1·b + 0.4·c ≤ 80 oven-hours.
- Problem type: LP, or a trivial MILP if cakes must be integers.
Solution
- Bread uses 300 × 0.1 = 30 oven-hours, leaving 50 hours.
- Each cake nets a positive $7, so the oven time left over goes to cakes: c = 50 / 0.4 = 125 cakes.
- The plan splits across the two ovens without trouble. For example, oven 1 bakes all 300 loaves and 25 cakes (30 + 10 = 40 h), and oven 2 bakes 100 cakes (40 h).
Plan: 300 loaves and 125 cakes. Profit = 300 × 2.50 + 125 × 7 = $750 + $875 = $1,625. Revenue is $2,700 and ingredient cost is $1,075. Both ovens are fully used at 80 of 80 hours.
Ambiguities
- "Plans to bake 300 loaves": I read this as exactly 300. If it meant at least 300, the answer changes. Bread earns $25 per oven-hour against $17.50 for cakes, so the plan would become 800 loaves and 0 cakes, with a profit of $2,000. Tell me if that is what you meant.
- "Earn": I read this as revenue, with cost subtracted. If $12 and $4 were already profits, the plan stays the same (300 loaves and 125 cakes) and the profit would be $2,700.
Concepts-only skill, so the trial gave the model only the Skill and Read tools. The model's arithmetic was checked by hand (300 loaves and 125 cakes, profit 1,625; 800 loaves if the commitment were a minimum). Nothing was compared against a no-skill run.
它做什麼
教模型根據文字描述的問題建立線性規劃（LP）、混合整數規劃（MILP）與二次規劃（QP）模型。只談概念，不涉及求解器介面，也不寫程式碼。
運作方式
- 把每句話歸類為參數、限制式、決策或目標，並區分「計畫生產」「擁有」這類已確定的說法與「可以」「考慮」這類可選的說法。
- 找出隱含的目標：只給成本時，「擬定計畫」代表成本最小化；同時給出成本與收入時，則是利潤最大化。
- 要求模型遇到歧義時先提問，或把所有合理的解讀都計算一遍並回報結果，而不是悄悄選一種。
- 涵蓋常見建模模式與陷阱：分段線性利潤搭配整數總量、下料問題的廢料、目標規劃、多期庫存、含共用混合工序的配料。
適合
作業研究的習題與實際的規劃問題：生產、排程、配料、投資組合、資源配置。
限制
只負責建模，不負責求解，搭配哪個求解器由你決定。套件內附 NVIDIA 自己的評測報告（是他們的評測，不是我們的），其中說明 cuOpt 的 QP 支援仍在 beta。
低風險：純指令檔，來自 NVIDIA 官方 Skills 儲存庫（Apache-2.0）。沒有腳本、不連網、不寫入檔案，也不需要帳號或金鑰。壓縮檔內另有 NVIDIA 自己的評測報告與一個簽章檔，我們原樣收錄，並未驗證該簽章。結果由模型產生：用於實際決策前，請自行核對模型與其中的數字。