Graph linear inequalities and systems of linear inequalities as half-plane solution regions.
Model a feasible region from a context
Problem
Let \(x\) be the number of small posters and \(y\) be the number of large posters. Small posters take \(2~\text{minutes}\) each, large posters take \(5~\text{minutes}\) each, there are \(\text{at}~\text{most}~40~\text{minutes}\), and \(\text{at}~\text{least}~8~\text{posters}\) are needed. Model the feasible region with linear inequalities.
Big Picture
What this problem is really about
The context supplies four distinct constraints, and each must keep its original variable meaning. We’ll attach each time coefficient to the matching poster count, translate the maximum time and minimum production phrases with the correct directions, and add nonnegativity because the variables count objects. The feasible region is the common overlap, not any one condition by itself.
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