Which of the following group of constraints represents the feasible region given as shaded area below ?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( x+2y\ge 7,2x+y\le 10,x,y\ge 0 \)
The line x + 2y = 7 meets the y-axis at (0, 3.5) and the line 2x + y = 10 at (0, 10). The shaded region lies between these two lines, to the right of the y-axis, so it is above x + 2y = 7 and below 2x + y = 10.
A test point inside the shaded region confirms this, for example (1, 5) (at x = 1 the lines are at y = 3 and y = 8):
\( \displaystyle x+2y=1+10=11\ge 7 \)
\( \displaystyle 2x+y=2+5=7\le 10 \)
So the constraints are \( x+2y\ge 7,\ 2x+y\le 10,\ x,y\ge 0 \).