Maths: Why Bulk Discounts Break Direct Proportion

Direct proportion describes a relationship where two quantities increase at a constant rate, so that cost divided by panels stays fixed. In pricing models, this means each additional item adds the same unit rate, expressed as cost = k × panels, where k is the constant of proportionality. Here, the given data lets us verify that ratio directly: if the cost per panel remains unchanged across different order sizes, the relationship is genuinely proportional. This matters because real-world pricing rarely stays linear forever. While small orders may fit a constant unit rate neatly, larger orders often involve bulk discounts that reduce the price per panel, breaking the proportional pattern. Understanding where a model holds and where it fails is central to critical evaluation: the constant ratio confirms proportionality for the given values, but the mechanism of discounting shows why extrapolating that same rate to much bigger orders can overestimate cost and mislead a company quoting prices at scale.