The feasible region for an LPP is shown in the given figure.
Constraints for the LPP are :
Answer & explanation
Correct answer: option 1
From the given graph, the shaded feasible region is bounded by the coordinate axes and two straight lines.
The corner points visible are:
O(0,0), C(0,20), B(20,10), A(25,0)
Equation of line CB through (0,20) and (20,10):
$\frac{y-20}{10-20}=\frac{x-0}{20-0}$
$y= -\frac{1}{2}x+20$
Equation of line BA through (20,10) and (25,0):
$\frac{y-10}{0-10}=\frac{x-20}{25-20}$
$y=-2x+50$
Hence the constraints of the LPP are:
$x \ge 0$
$y \ge 0$
$y \le -\frac{1}{2}x+20$
$y \ge -2x+50$ is NOT included since region lies below this line
$x \le 25$ (from point A)
final answer: The constraints are $x\ge0,\; y\ge0,\; y\le -\frac{1}{2}x+20,\; y\le -2x+50,\; x\le25$