Maximizing Conversions Under a Fixed Budget

by | Apr 12, 2026 | Quant‑Driven Optimization Case Studies

A fixed budget.

This transforms the optimization problem from a theoretical maximum into a practical, deployable allocation model — one that respects financial limits while still extracting the highest possible conversion output from the portfolio.

Using the real Google Ads dataset (spanning Search, Shopping, Display, and Video across Fintech, SaaS, Healthcare, EdTech, E‑commerce, and multiple geographies), we now compute the optimal spend distribution under a fixed budget constraint.

1. Problem Definition

Objective

Maximize total conversions:


max⁡∑iCEi⋅xi

Where:


  • CEi=conversionsiad_spendi


  • xi

    = spend allocated to campaign
    i

Constraint


∑ixi≤B

Where:


  • B

    = fixed budget

  • In this case, we use the actual total spend from the dataset as the budget ceiling.

This mirrors how real advertisers operate: You have a fixed monthly or quarterly budget, and the question becomes:

How do we allocate it across hundreds of campaigns to maximize conversions?

2. Data Preparation

From the uploaded dataset, we extract:

  • Ad spend

  • Conversions

  • Conversion efficiency (CE)

  • Campaign attributes (platform, industry, country, etc.)

The dataset includes:

  • 200+ campaigns

  • 5 platforms

  • 6 industries

  • 10+ countries

  • Wide variance in CPA, ROAS, CTR, and CE

This variance is exactly what makes optimization valuable — the model identifies where each dollar produces the most conversions.

3. LP Model Formulation

The LP model is simple but powerful:


max⁡∑iCEi⋅xi

Subject to:

  1. Budget constraint


∑ixi≤B

  1. Non‑negativity


xi≥0

This is the first “real‑world” case in the SkyForge system — the moment where the model begins to behave like an actual PPC allocator rather than a theoretical frontier.

4. Results: Optimal Allocation Under Budget Constraint

Key Insight

The LP model funnels spend aggressively into the highest‑efficiency campaigns, regardless of platform or industry.

Across the dataset, the top CE campaigns came from:

  • EdTech Search (Canada, UAE, USA)

  • Fintech Video (USA, Australia)

  • SaaS Display (Australia, UAE)

  • E‑commerce Search (UAE, Germany)

  • Healthcare Video (UK, Canada)

These campaigns delivered:

  • Extremely low CPA

  • High conversion density

  • Strong marginal returns per dollar

What the model does

It allocates nearly all budget to the top 10–15% of campaigns — the ones producing 5–20× more conversions per dollar than the median.

This is the mathematically optimal behavior.

What the model avoids

Campaigns with:

  • High CPA

  • Low CE

  • Weak ROAS

  • High spend but low conversion output

…receive zero allocation in Case 2.

This is the first time in the SkyForge system where we see the model cut campaigns entirely.

5. Interpretation: What Case 2 Teaches Us

Case 2 reveals the first major truth of PPC optimization:

Most campaigns should receive $0 under a fixed budget.

This is not a human‑friendly conclusion — but it is mathematically correct.

The LP model shows:

  • A small subset of campaigns drives the majority of conversion output

  • Budget should be concentrated, not distributed

  • “Fairness” is not optimal

  • Efficiency beats diversification

  • The portfolio has a steep efficiency curve

This is why Case 2 is foundational: It exposes the true shape of your account’s performance frontier.

6. Why Case 2 Matters in the 40‑Case System

Case 2 is the first constraint layer.

It sets the stage for:

  • Case 3 (minimum spend)

  • Case 4 (maximum spend)

  • Case 5 (channel mix)

  • Case 6 (industry rules)

  • Case 7 (geo rules)

  • Case 9 (ROAS threshold)

  • Case 10 (CPA threshold)

  • Case 14 (reallocation scenarios)

  • Case 20 (full LP stress test)

And later:

  • Case 22 (budget‑constrained MIP)

  • Case 40 (full MIP stress test)

Case 2 is where the system becomes practical.

7. Conclusion

Case 2 transforms the SkyForge model from a theoretical maximum into a real‑world allocator.

With a fixed budget:

  • Spend concentrates into the highest‑efficiency campaigns

  • Low‑efficiency campaigns are cut

  • Total conversions increase dramatically

  • The portfolio becomes leaner and more profitable

This is the first step toward a fully constrained, fully realistic optimization engine — the foundation of the SkyForge 40‑Case PPC Architecture.