question_answer

The feasible region represented by\[{{x}_{1}}+{{x}_{2}}\le 1\],\[-3{{x}_{1}}+{{x}_{2}}\ge 3,\,\,({{x}_{1}},\,\,{{x}_{2}}\ge 0)\]is

A)  a polygon          

B)  a singleton set

C)  empty set        

D)  None of these

Correct Answer: C

Solution :

Given inequalities are                 \[{{x}_{1}}+{{x}_{2}}\le 1,\,\,-3{{x}_{1}}+{{x}_{2}}\ge 3,\,\,({{x}_{1}},\,\,\,{{x}_{2}}\ge 0)\] It is clear from the graph that no feasible region are there. Hence, it is empty set.