MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
Study the system of inequalities given below:
x+y≥3,x−y≤1,2x+y≤8,x≥0,y≥0.
(i) Write down every point of intersection that can arise from any two of the five boundary lines, restricting your list to points lying in the first quadrant.
(ii) For each point obtained in part (i), test whether it satisfies all five inequalities. Create a clearly labelled table of your results.
(iii) Hence list, in ascending order of the x-coordinate, all vertices of the feasible region determined by the system.
(iv) Draw a neat, labelled sketch of the feasible region, marking and naming every vertex found in part (iii).