In the solution region \(x+y\geq 6\), \(2x+y\geq 7\), \(0\leq x\leq 4\), and \(y\geq 0\), what is the minimum value of (y)?

Correct answer: 2

To obtain the minimum value of \(y\), take the largest allowed value of \(x\), namely \(4\). Then \(x+y\geq 6\) gives \(y\geq 2\). Also, substituting \(x=4\) in \(2x+y\geq 7\) gives \(y\geq -1\), while \(y\geq 0\) is already given. Combining all the lower bounds gives \(y\geq 2\), so the minimum value is \(2\). The point \((4,2)\) satisfies every inequality. Exam tip: when minimizing a variable, compare all lower bounds imposed by the constraints.