Choose between cost and quality
Which options can be rejected without choosing a preference weight?
Entering midway? With multiple objectives, improving one quantity may worsen another. State which direction is better for each.
Start with a concrete question
Five authored alternatives have cost and fixture quality units. Compare dominance, a quality floor and explicit weighted preferences.
Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.
Go directly to the experiment · Review prerequisite mathematics and return here
What do you expect?
Predict before calculating: Which options can be rejected without choosing a preference weight?
Change one thing. Inspect what happens.
- Find the alternative worse in both cost and quality.
- Change the preference weight and observe which nondominated option wins.
- Apply a minimum-quality constraint.
- Write a recommendation stating weights, units and a sensitivity check.
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Cost–quality alternatives
Horizontal: cost (credits). Vertical: fixture quality units.
- 1. A (points)
- 2. B (points)
- 3. C (points)
- 4. D (dominated) (points)
- 5. E (points)
Axes use the displayed ranges.
Read plotted values as a table
| Series | cost (credits) | fixture quality units |
|---|---|---|
| A | 2 | 3 |
| B | 4 | 6 |
| C | 7 | 9 |
| D (dominated) | 6 | 5 |
| E | 9 | 10 |
Follow the calculation
- A: cost 2, quality 3; nondominated; eligible; weighted score=0.5.
- B: cost 4, quality 6; nondominated; eligible; weighted score=1.
- C: cost 7, quality 9; nondominated; eligible; weighted score=1.
- D: cost 6, quality 5; dominated; eligible; weighted score=-0.5.
- E: cost 9, quality 10; nondominated; eligible; weighted score=0.5.
- Selected B; ties favor lower cost.
Pareto dominance rejects an option only when another is no worse on every stated objective and better on at least one. Selecting among nondominated options requires declared preferences and units.
Defend a constrained recommendation
State the objective directions, feasible options, a dominance argument, your preference assumption and a condition that changes your decision. Do not call the numeric fixture quality a verified real-world score.
80/8,000 characters. Drafts save locally and are included in backups. Importing or opening a draft never runs it.
Compare with my earlier draft
D looks best to me. The weighted score proves it is objectively the best option.
Explain what you changed and why in your observation notes. Text differences do not establish quality.
Inspect an example solution after your attempt
B dominates D because it costs less (4<6) and has greater fixture quality (6>5). Among A,B,C,E, choose using a declared quality floor and preference weight; test nearby weights. A weighted score reflects chosen units and preferences, not universal optimality.
This is one worked example. Test another input and explain its limitations.
Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.
Explain the mechanism
Choose between cost and quality
Five authored alternatives have cost and fixture quality units. Compare dominance, a quality floor and explicit weighted preferences.
Concepts to recall
With multiple objectives, improving one quantity may worsen another. State which direction is better for each.
Understand the mechanism
B costs 4 with quality 6; D costs 6 with quality 5. B dominates D.
A, B, C and E trade higher cost for higher quality; no single choice wins every preference.
The weighted score combines assumed comparable numerical scales. Rescaling quality without adapting weights changes the decision, so weights are not objective facts.
Symbols and calculation
Score=w·quality−(1−w)·cost, where 0≤w≤1. Dominance requires no higher cost and no lower quality, with at least one strict improvement.
Worked example
A: cost 2, quality 3; nondominated; eligible; weighted score=0.5.
B: cost 4, quality 6; nondominated; eligible; weighted score=1.
C: cost 7, quality 9; nondominated; eligible; weighted score=1.
D: cost 6, quality 5; dominated; eligible; weighted score=-0.5.
E: cost 9, quality 10; nondominated; eligible; weighted score=0.5.
Selected B; ties favor lower cost.
Your investigation
Find the alternative worse in both cost and quality.
Change the preference weight and observe which nondominated option wins.
Apply a minimum-quality constraint.
Write a recommendation stating weights, units and a sensitivity check.
Limits and interpretation
- These are bounded teaching models with explicit assumptions, not evidence of a real-world intervention.
Try a fresh case
Option P costs 3 and has quality 8; Q costs 5 and quality 7; R costs 2 and quality 6. How many options are nondominated?
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
Explain a fresh small numerical case with a diagram or table and an argument.
College investigation
Implement the method, test a boundary or counterexample, and justify its assumptions.
Workplace investigation
Use a small decision scenario, state units and constraints, and test how the recommendation changes.
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.