question_answer

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

A)  a polygon        

B)  a singleton set

C)  an 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 there is no feasible region. Hence, it is an empty set.