Consider the following statements about systems of linear inequalities in two variables.
MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming
Problem
Consider the following statements about systems of linear inequalities in two variables.
(i) Define the term "feasible region" for a system of linear inequalities.
(ii) For the system x+y≤5 and x+y≥10 , prove that no ordered pair (x,y) satisfies both inequalities simultaneously.
(iii) Let a and b be real numbers. Obtain the necessary and sufficient condition on a and b so that the two inequalities x+y≤a and x+y≥b possess at least one common solution in real numbers.