During a corporate finance workshop for logistics managers, you are reviewing different cost-benefit models. You need to identify mathematical models that represent constraints with varying rates in the denominator. Based on your knowledge of algebraic models, which of the following is an example of a rational inequality?

An operations manager uses the inequality $\frac{800}{h} \leq 40$ to ensure that the hourly production cost for a factory remains within a set budget, where $h$ represents the total operating hours. True or False: This mathematical statement is an example of a rational inequality.

Classifying Safety Constraints

As a business operations analyst for a manufacturing firm, you are organizing a database of mathematical models used for resource allocation and cost-threshold analysis. Match each mathematical statement to its correct algebraic classification based on its structure.

A project manager at a manufacturing firm uses the mathematical statement $\frac{4500}{x} + 12 \leq 60$ to determine the number of units $x$ that must be produced to keep the average cost within a specific budget. Because this statement features a variable in the denominator of a fraction and an inequality symbol, it is categorized as a ________ inequality.