Maths. Section B1Linear Programming

For the constraints x+y≤ 60,\ 5x+y≤ 100 and x≥ 0,y≥ 0 , the feasible…

For the constraints $ x+y\le 60,\ 5x+y\le 100 $ and $ x\ge 0,y\ge 0 $, the feasible region is:

$Lines x + y = 60 and 5x + y = 100 dividing the first quadrant into regions P, Q, R and S$

Answer & explanation

Correct answer: option 3

The correct answer is Option (3) → R

Both constraints are of the form “≤”, and the origin satisfies both (0 ≤ 60 and 0 ≤ 100). So the feasible region is the part of the first quadrant that is on the origin’s side of both lines.

P is above x + y = 60, so it fails the first constraint.
Q is above both lines.
S is to the right of 5x + y = 100, so it fails the second constraint.
R is below both lines, touching the origin.

So the feasible region is R.

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

$NCERT extract$