Equation 17 · Part 1 · AI Inference Economics in Practice: An Advanced Technical Guide

Symbol u^*

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

u^{*}

What this part means

$u^*$ is the quantity selected or evaluated by the optimization written on the right.

Its job in the formula

$u^*$ is the quantity selected or evaluated by the optimization written on the right.

Full expressionSymbol u^*Article 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

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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