Equation 17 · Part 7 · AI Inference Economics in Practice: An Advanced Technical Guide

subscript

u^{*} = \frac{P_r}{Q_{\max}\, c_{\mathrm{od}}}

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle meaning

The passage around this formula

The arithmetic is simple once both prices are in hand, and generalizes across any reserved-capacity product structured this way. Let $P_r$ be the reserved capacity’s price per hour, $Q_{\max}$ the maximum throughput it sustains per hour at full utilization, and $c_{\mathrm{od}}$ the effective on-demand cost of the equivalent work. At actual utilization u , the effective cost per unit under reservation is $P_r$ / (u \, $Q_{\max}$ ) , and reservation wins exactly when $u^{*} = \frac{P_r}{Q_{\max}\, c_{\mathrm{od}}}$ . is cleared. Utilization above $u^*$ favours reservation; below it favours paying as you go. The formula’s value is what it forces a team to measure honestly before signing: not peak throughput or a favourable week’s…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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