The feasible region for an LPP is shown in the given figure. Constraints for the LPP are : |
$2x+y≤50, x+2y ≤ 40, x ≥ 0, y ≥ 0$ $2x+y≥50, x+2y ≥ 40, x≥ 0, y ≥ 0$ $2x+y≤50, x+2y ≥ 40, x≥ 0, y ≥ 0$ $2x+y≥50, x+2y ≤ 40, x≥ 0, y ≥ 0$ |
$2x+y≤50, x+2y ≤ 40, x ≥ 0, y ≥ 0$ |
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 $x\ge0,\; y\ge0,\; y\le -\frac{1}{2}x+20,\; y\le -2x+50,\; x\le25$ |