Consider the following system of linear inequalities in two variables:
MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
Consider the following system of linear inequalities in two variables:
2x+y≥6,x+2y≥6,x≥0,y≥0.
(i) Rewrite each inequality as its corresponding boundary line and draw all four boundary lines on the same pair of axes.
(ii) Shade the portion of the plane that represents the set of points satisfying the complete system of inequalities.
(iii) Determine the coordinates of every vertex of the shaded region, showing all algebraic working needed to obtain each coordinate.
(iv) List the vertices in clockwise order, starting with the vertex that lies on the y-axis.