MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
In the first quadrant, a quadrilateral region is bounded by the coordinate axes and the two oblique lines 2x+y=10andx+2y=12. The line 2x+y=10 is drawn with a solid line, while the line x+2y=12 is drawn with a dotted line. The region consists of all points that lie beneath both oblique lines and between the axes.
(i) Write an inequality corresponding to each oblique line that selects the correct half-plane.
(ii) Include the appropriate inequalities for the coordinate axes and hence write the full system describing the quadrilateral region.
(iii) Determine the x- and y-intercepts of each oblique line and use them to justify that the region is bounded.
(iv) Decide whether the point (3,2) lies on a boundary, inside the region, or outside it, giving reasons for your answer.