Which point lies in the feasible region of (x\ge 1), (y\ge 2), (x+y\le 7)?

Correct answer: ((2,4))

The direct answer is option A,
\((2,4)\). A feasible region contains only points that satisfy every inequality at the same time. Test option A step by step:
\(x=2\ge1\) is true,
\(y=4\ge2\) is true, and
\(x+y=2+4=6\le7\) is true. Thus it belongs to the feasible region. Option B,
\((0,4)\), satisfies the y-condition and the sum condition, but fails
\(x\ge1\) because
\(0<1\). Option C,
\((3,5)\), satisfies the first two conditions, but
\(3+5=8>7\), so it fails the third. Option D,
\((4,1)\), satisfies
\(x\ge1\), but fails
\(y\ge2\) because
\(1<2\). Therefore only A works. Exam cue: for a feasible point, check every inequality, not just most of them.