A plan must survive its resource constraints
Can a high-output land plan still work when water falls short?
Entering midway? Revisit An efficient replacement has an upfront cost for the preceding worked example, or start here and use the explanation below.
Start with a concrete question
Original synthetic scenario. Ten divisible plots can be habitat, dry farmland or irrigated farmland. Irrigation uses five water units per plot; food and a habitat index use explicit synthetic rules.
Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.
What do you expect?
Will requesting irrigation for more plots increase output when the water budget is already exhausted?
Change one thing. Inspect what happens.
- At defaults check that habitat, irrigated and dry plots add to ten.
- Raise requested irrigation until a land or water constraint binds.
- Apply a 40% water reduction and compare realized output with the original plan.
- Choose a plan with a stated habitat floor and food target; report whether it remains feasible under drought.
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Compare the current results
Every bar starts at zero and uses the same numeric scale in this chart. The upper bound automatically adjusts to the largest current value (at least 1), so compare the numbers when changing inputs. Units and quantities come from each label; different kinds of quantity are not interchangeable. Displayed values are rounded to at most six significant digits.Follow the calculation
- Ten plots: habitat 4, farmland 10 − 4 = 6.
- Available water = 24 × (1 − 0) = 24 units.
- Irrigated plots = min(farmland 6, requested 4, water/5 4.8) = 4.000.
- Food = irrigated 4.000 × 8 + dry 2.000 × 3 = 38.000.
- Invented habitat index = habitat² = 16; this is a teaching objective, not an ecological measurement.
A single objective hides trade-offs between output, water, and habitat. Stress-test a proposed allocation against reduced water instead of assuming the planned irrigation is available.
Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.
Explain the mechanism
What the experiment explains
Original synthetic scenario. Ten divisible plots can be habitat, dry farmland or irrigated farmland. Irrigation uses five water units per plot; food and a habitat index use explicit synthetic rules.
A resource constraint limits what can actually be used, independently of what is requested. The model takes the minimum of farmland, requested irrigation and water-supported area.
At defaults habitat is four, farmland six and irrigated area four. Two dry plots remain. Food is 4×8+2×3=38 and water use is 4×5=20.
The habitat index is deliberately nonlinear: habitat². It illustrates a competing objective, not a measured ecological relationship. A defensible decision must disclose that assumption and avoid combining unrelated units without a justified value model.
Read the relationship
Irrigated = min(10−habitat, requested irrigation, available water/5). Food = 8×irrigated + 3×dry plots. Habitat index = habitat².
Inspect the evidence
The numerical trace is recalculated from your current settings. Compare a controlled pair of trials before changing several inputs together. Inspect intermediate quantities as well as final metrics; state which assumptions make the comparison meaningful.
Boundaries of the model
- Divisible homogeneous land, invented yield/index rules and no spatial habitat connectivity.
- No crop prices, soil change, irrigation timing, legal entitlements or empirical ecological calibration.
Return to the environment and sustainability course and project to connect this mechanism to the broader investigation.
Try a fresh case
A new 10-plot plan keeps 3 habitat plots, requests 5 irrigated plots, and has 15 water units. Using 5 water per irrigated plot, yields 8 irrigated and 3 dry, what is total food?
This is a public practice check. Retries support learning; matching a number does not certify independent proficiency.
Take the investigation further
Choose any extension. These are project prompts for you to carry out; they are not automatically assessed.
School investigation
Find two feasible plans and explain which outcome each favors.
College investigation
Enumerate the Pareto frontier under several drought scenarios and verify constraints independently.
Workplace investigation
Prepare a resource-allocation brief with minimum service/ecological requirements and a drought contingency.
Keep the evidence, choose your next step
Completion records your own decision that you have worked through this investigation. Practice checks and independent project evidence are separate.