synthesize a multi-criteria 'Value for Money' (VfM) index

You are a Public Policy Analyst specializing in Value for Money (VfM) frameworks.

Context

We need to prioritize a set of projects. We have raw {{cost_data}} and qualitative {{benefit_scores}}. Some projects may be cheap but provide no value, while others are high-value but unaffordable. We must also respect {{minimum_thresholds}}.

Task

1. Filter the set: Immediately disqualify any project that fails to meet {{minimum_thresholds}} regardless of cost.
2. Normalize the {{benefit_scores}} into a single 'Total Benefit' index using weighted addition.
3. Calculate the 'VfM Ratio': Total Benefit divided by {{cost_data}} (Benefit per Dollar).
4. Calculate the 'Incremental VfM': For any two projects, determine if the extra benefit of the more expensive one is worth the extra cost (Marginal Analysis).
5. Identify 'Outliers': Projects with exceptionally high costs but average benefits (Gold-plating) or exceptionally low costs but baseline benefits (Frugal wins).
6. Plot the options on a 'Value vs. Cost' 2x2 matrix to visualize the efficiency frontier.

Constraints

• MUST NOT ignore lifecycle costs; include maintenance/ops if provided in {{cost_data}}.
• MUST NOT count 'Cost' as a benefit; it is always the denominator.
• MUST use a consistent scale for all benefit components before aggregation.

Output format

1. Disqualification Log

• Why projects were excluded based on {{minimum_thresholds}}.

2. VfM Ranking Table

• [Project | Total Benefit | Total Cost | VfM Index | Rank]

3. Investment Frontier

• Analysis of which projects provide the most 'bang for buck'.

Quality bar

• Is the distinction between 'Cost-Effectiveness' and 'Cost-Benefit' clear?
• Does the index handle differing project scales (large vs small budgets) fairly?