Equation 17 · Part 2 · AI Inference Economics in Practice: An Advanced Technical Guide

Symbol P_r

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

P_r

What this part means

the reserved capacity’s price per hour.

Its job in the formula

$P_r$ occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Full expressionSymbol P_rArticle meaning

Where the article explains it

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.

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…

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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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