Mathematics
Mathematics
Problem
Examine the system of inequalities (i) Sketch accurately the feasible region determined by the above inequalities. (ii) Prove that the feasible region obtained in part (i) is a convex set. (iii) List the vertices of the feasible region in order of increasing –coordinate.Intuitive explanation
Linear inequalities carve out a region in the plane bounded by straight lines. The feasible region is where all constraints overlap simultaneously—think of it as the intersection of half-planes. To find it, sketch each boundary line, shade the correct side for each inequality, and identify where all shaded regions meet. The vertices (corners) of this region occur where pairs of boundary lines intersect, and they're crucial because they often contain optimal solutions.
Intuitive explanation
Linear inequalities carve out a region in the plane bounded by straight lines. The feasible region is where all constraints overlap simultaneously—think of it as the intersection of half-planes. To find it, sketch each boundary line, shade the correct side for each inequality, and identify where all shaded regions meet. The vertices (corners) of this region occur where pairs of boundary lines intersect, and they're crucial because they often contain optimal solutions.