MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
Consider the constraint set S1:
2x+y≤8,
x+2y≤8,
x≥0, y≥0.
(i) Find the coordinates of all corner points (vertices) of the feasible region of S1.
(ii) The designer replaces only the first inequality with 2x+y≤10, forming a new set S2 while keeping the other three inequalities unchanged. Find the new set of corner points of the feasible region of S2.
(iii) Compute the exact area of each feasible region and hence find by how much the area changes.
(iv) Identify the single constraint responsible for the change and explain briefly why no other constraint needed to be altered to obtain the new region.