In the linear programming problem maximize \( z=4x+3y \) subject to the constraints \( x+y\ge 8 \), \( 3x+5y\le 15,\ x\ge 0,y\ge 0 \) , the feasible region has
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → No point
The constraint \( 3x+5y\le 15 \) with \( x,y\ge 0 \) allows only the triangle with corners (0, 0), (5, 0) and (0, 3).
On this triangle, x + y is largest at (5, 0), where x + y = 5. So \( x+y\ge 8 \) can never hold there.
No point satisfies all the constraints, so the feasible region is empty.
NCERT (2026-27 edition):
Graphical Method of Solving Linear Programming Problems
