Create equations in two or more variables and graph them with appropriate labels and scales.
Build and graph a constraint equation or inequality
Problem
Graph the feasible region for a budget of \(\text{at}~\text{most}~\$100\) when each \(x\)-item costs \(\$4\) and each \(y\)-item costs \(\$5\) and \(x\) and \(y\) are nonnegative integers. Use the displayed coordinate plane, and justify the inequality, boundary, intercepts, and shaded side.
The budget constraint starts by adding each item’s unit cost times its count. We’ll translate “at most” with an inclusive inequality, use the equality case to draw a solid boundary through its intercepts, test the origin to find the affordable side, and retain only nonnegative integer points because both variables count items.
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