使用Excel计算含四个未知变量的方程及工厂工人分布投影

Hey, I feel your frustration—spending a week and a half stuck on a problem without that key insight is such a grind. Let’s break down some actionable directions to nudge you forward, without dumping a full solution on you:

• First, formalize your existing distribution’s core metrics
  You’ve got four factory size categories from a base year. Before projecting, clarify what exactly you’re preserving:

  • Is it the percentage of factories falling into each size bracket?
  • Or the percentage of total workers employed in each bracket?
    Write these down as explicit ratios (e.g., "35% of all factories are in Size Category 1, employing 12% of total workers")—this will make scaling easier later.

• Use your C = A/B metric as a scaling anchor
  The average workers per factory is the biggest link between your base data and target datasets. Here’s how to tie it in:

  • If the target dataset’s C is close to your base year’s, you might start with a direct ratio projection (e.g., apply base year’s factory bracket percentages to target B to get bracket counts, then adjust worker counts to hit target A).
  • If C differs significantly, try a quantile matching approach: map the base year’s size bracket quantiles (e.g., 25th percentile factory size) to the target C’s expected quantiles. For example, if base year’s median factory size is 1.2x C_base, set target median size to 1.2x C_target.

• Test with a tiny, hypothetical target dataset
  Grab a small, made-up example to validate logic: say target A=4000, B=100 (so C=40). If your base year has 20% of factories in the "1-20 workers" bracket, try assigning 20 factories to that bracket, then calculate what average worker count per factory in that bracket would let you hit the total A. This will reveal gaps in your scaling logic fast.

• Lock in any hard constraints
  Do your target datasets have non-negotiable rules? E.g., "no factory in this industry can have more than 200 workers" or "at least 10% of factories must be micro-sized"? These constraints will narrow down which scaling methods are feasible—you might need to tweak bracket ratios to stay within bounds while still hitting A and C.

内容的提问来源于stack exchange，提问作者GeneralAlzheimer