What is the solution region of \(x\geq 0\), \(y\geq 5\), and \(x+y\leq 4\)?

Correct answer: Empty region

Since \(x\geq 0\) and \(y\geq 5\), it must follow that \(x+y\geq 5\). However, the third inequality requires \(x+y\leq 4\), which is incompatible with this condition. Therefore, no point satisfies all three inequalities simultaneously, so the solution region is empty. Even on the boundary line \(x+y=4\), \(y\geq 5\) is impossible when \(x\geq 0\). Exam tip: Compare minimum and maximum possible values to spot an inconsistency quickly.