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The rapid growth of AI and HPC workloads is sharply increasing data center electricity use and carbon emissions, yet infrastructure decisions still treat cost, performance, and sustainability as separate concerns. To bridge this gap, we introduce the Carbon and Economy Optimization in Data Centers (CEO-DC). CEO-DC is an integrated framework to guide operators, hardware designers, and policymakers toward balanced, climate-conscious compute growth. It captures key trade-offs across hardware procurement, performance scaling, costs, electricity carbon intensity, and decarbonization trends, and defines two metrics—Carbon Efficiency (FLOP/tCO₂-eq) and Price Efficiency (FLOP/$)—to evaluate hardware upgrades. Applying CEO-DC across AI accelerator generations and regional grid scenarios, we show how carbon intensity, efficiency gains, and upgrade timing shape sustainable capacity expansion. Short upgrade cycles rarely reduce net emissions without strong carbon incentives, with high carbon intensity (CI) regions benefiting most and low-CI regions seeing diminishing returns. Our analysis highlights three requirements for sustainable scaling: improving hardware cost and carbon efficiency, aligning upgrades with grid decarbonization, and enabling policies that balance economic and environmental objectives.