A tailor stitches x shirts and y kurtas a week. A shirt takes 5 hours and a kurta takes 4 hours, and he can work at most 40 hours a week. With \(x \ge 0,\ y \ge 0\), the corner points of the feasible region are
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (0, 0), (8, 0) and (0, 10)
The time constraint is
\(5x + 4y \le 40\)
Together with \(x \ge 0,\ y \ge 0\), the feasible region is the triangle cut off by the line \(5x + 4y = 40\) in the first quadrant. The line meets the axes at
\(y = 0:\ 5x = 40,\ x = 8\)
\(x = 0:\ 4y = 40,\ y = 10\)
The origin satisfies \(0 \le 40\), so it is also a corner. The corner points are (0, 0), (8, 0) and (0, 10).
Why the other options are incorrect
Option (1) (0, 0), (10, 0) and (0, 8) — Incorrect. The intercepts are swapped: \(5(10) = 50 \gt 40\).
Option (3) (0, 0), (8, 0) and (0, 8) — Incorrect. \(4(8) = 32 \lt 40\), so (0, 8) is not on the boundary line.
Option (4) (8, 0) and (0, 10) only — Incorrect. The origin is also a corner, where the two axes meet.