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.
它做什么
教模型根据文字描述的问题建立线性规划（LP）、混合整数规划（MILP）和二次规划（QP）模型。只讲概念，不涉及求解器接口，也不写代码。
工作方式
- 把每句话归类为参数、约束、决策或目标，并区分“计划生产”“拥有”这类已确定的说法与“可以”“考虑”这类可选的说法。
- 找出隐含的目标：只给成本时，“制定计划”意味着成本最小；同时给出成本和收入时，则是利润最大。
- 要求模型遇到歧义时先提问，或把所有合理的理解都算一遍并报告结果，而不是悄悄选一种。
- 覆盖常见建模模式和陷阱：分段线性利润加整数总量、下料问题的废料、目标规划、多期库存、带共用混合工序的配料。
适合
运筹学作业和真实的计划问题：生产、排程、配料、投资组合、资源分配。
局限
只负责建模，不负责求解，配合哪个求解器由你决定。包内附带 NVIDIA 自己的评测报告（是他们的评测，不是我们的），其中说明 cuOpt 的 QP 支持仍处于 beta。
低风险：纯指令文件，来自 NVIDIA 官方 Skills 仓库（Apache-2.0）。没有脚本、不联网、不写文件，也不需要账号或密钥。压缩包里还有 NVIDIA 自己的评测报告和一个签名文件，我们原样收录，没有验证过这个签名。结果由模型生成：用于真实决策前，请自己核对模型和其中的数字。