SCIENCE · INVESTIGATE AND EXPLAIN

Compare cost efficiency without losing total-service constraints

An intervention comparison needs a shared service definition, duration and cost boundary. A low cost per unit of nominal improvement may not deliver enough total improvement, and nominal performance may not persist under actual conditions. Costs alone also omit ecological side effects and distributional consequences.

Learning outcome: Compare all three options at fixed realization 0.75, then reduce realization to 0.5. State a service threshold and identify which options remain feasible before comparing their ratios.

Starting recap

Preserve packet identity, independent units, analysis recipe, outcome constraints and review authority; distinguish scientific uncertainty from stakeholder value choices.

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Try

Candidate B at realization 0.75 reduces 37.5 kg/day at 200 cost units/year, ratio 200/37.5≈5.333. A at the same factor reduces 22.5 at 90, ratio 4, but cannot meet a 35 kg/day requirement by itself.

Open the experiment

Predict

The smallest unit-cost ratio necessarily identifies:

Your prediction and reason

Experiment

Compare all three options at fixed realization 0.75, then reduce realization to 0.5. State a service threshold and identify which options remain feasible before comparing their ratios.

Compare cost per verified service under uncertain performance

Worked teaching model · synthetic values · Original alternatives A/B/C nominal load reductions 30/50/60 kg/day and annualized costs 90/200/360 cost units. Compare cost per kg/day of sustained reduction; factor applies to performance only. Costs share the same time convention and service scope. No currency, market price or real intervention recommendation.

Candidate:A0,B1,C2: 1 candidate code Realized fraction of nominal reduction: 0.75 fraction

Reset keeps your prediction, captures and practice history.

Original synthetic system; units differ by row
Quantity	Value	Unit
Nominal sustained load reduction	50	kg/day
Realized sustained load reduction	37.5	kg/day
Annualized cost	200	cost units/year
Cost per unit daily reduction capacity	5.333333	(cost units/year)/(kg/day)
Unrealized nominal reduction	12.5	kg/day

A low unit cost does not guarantee that an option meets the required total service.

Compare equal duration and load definitions; cost per kg actually removed over a year would divide by the number of operating days as well. Environmental side effects, distributional constraints and feasibility are not represented by this one efficiency ratio.

Predict, change one control, and retain contrasting captures. Reconstruct the analysis and decision rule before opening feedback. Display precision is not measurement precision.

A low unit cost does not guarantee that an option meets the required total service.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Define the decision and evidence boundary

Reconstruct the transparent method

The original alternatives A,B,C offer nominal sustained load reductions 30,50,60 kg/day with annualized costs 90,200,360 cost units/year. A supplied realization factor multiplies reduction but not cost. Cost divided by realized daily reduction has units(cost units/year)/(kg/day), a cost per unit of sustained daily reduction capacity.

Interpret the comparison

This metric is not yet cost per kilogram actually removed in a year. That would additionally divide by operating days, assuming the reduction persists for those days. A common duration preserves rankings, but unequal uptime can change them. Concentration changes from the paired dataset cannot be substituted for these load reductions without flow information.

Predeclare limitations and revision

A service requirement, budget constraint or hard ecosystem limit should be checked before selecting an apparently efficient option. Performance uncertainty, maintenance, rebound, transferred impacts and who bears costs need explicit evidence. These fictional cost units are not prices or financial advice, and no real treatment action is requested.

Worked original packet

Investigation

Compare all three options at fixed realization 0.75, then reduce realization to 0.5. State a service threshold and identify which options remain feasible before comparing their ratios.

Changed-case transfer

Candidate C at realization 0.5: find realized reduction, unrealized nominal reduction and cost ratio. Does it meet a 35 kg/day target?

Feedback

Realized 30 and unrealized 30 kg/day; ratio 360/30=12(cost units/year)/(kg/day). It misses 35 despite having the largest nominal reduction.

Sources and evidence boundary

Original prose, dataset and numerical exercises. Primary method/mechanism source, checked 30 October 2026. The versioned packet is synthetic, not observed fieldwork. No treatment implementation, site access, pollutant handling or real management authorization is requested. Preserve first reasoning and critique in the course workspace.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Candidate C at realization 0.5: find realized reduction, unrealized nominal reduction and cost ratio. Does it meet a 35 kg/day target?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Plan precision using independent units rather than repeated readings Next: Separate scientific forecasts from value choices in a score

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