Represent constraints and systems, then interpret viable and non-viable solutions in modeling contexts.
Write a rational constraint for a rate or resource context
Problem
Average cost is \(500/x~+~8\) and must be at most \(20\). Write the rational constraint and feasible domain.
Big Picture
What this problem is really about
Preserve the average-cost expression exactly, including which term is divided by the resource quantity. The phrase “at most” creates an inclusive upper bound. State the positive resource domain before manipulating the inequality, because that domain both prevents division by zero and determines whether multiplying by the variable would preserve the inequality direction.
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