Which point lies in the solution region of (x+5y\ge 15)?

Correct answer: ((5,2))

The direct answer is option A: \((5,2)\). To test a point in \(x+5y\ge15\), substitute its coordinates and compare the result with 15. For A, \(5+5(2)=5+10=15\), so the inequality is true because equality is allowed. Thus A lies on the boundary and is included in the solution region. For B, \((4,1)\), the expression is \(4+5=9\), and \(9\ge15\) is false. For C, \((0,2)\), it is \(0+10=10\), also less than 15, so it is outside. For D, \((10,0)\), it is \(10+0=10\), again outside. Therefore only A works. The boundary is \(x+5y=15\); the solution side contains values giving at least 15. Exam cue: substitute carefully and remember equality is included for \(\ge\).