The linear constraints for which the shaded region in the figure are:

The correct answer is Option (3) → \( x+3y\le 60,x\ \le y\ ,\ x+y\ge 10,x\ge 0,y\ge 0 \)

A test point inside the shaded region, such as (2, 12), shows on which side of each boundary line the region lies.

x + 3y = 60: the region is below this line; at (2, 12), 2 + 36 = 38 ≤ 60, so \( x+3y\le 60 \).
y = x: the region is above this line (towards the y-axis); at (2, 12), 2 ≤ 12, so \( x\le y \).
x + y = 10: the region is above this line, away from the origin; at (2, 12), 14 ≥ 10, so \( x+y\ge 10 \).

Together with \( x,y\ge 0 \), these are the constraints in Option (3).

NCERT (2026-27 edition):
Graphical Method of Solving Linear Programming Problems