question_answer

For the L.P. problem Min\[z={{x}_{1}}+{{x}_{2}}\] such that \[5{{x}_{1}}+10{{x}_{2}}\le 0,\ \ {{x}_{1}}+{{x}_{2}}\ge 1,\ \ {{x}_{2}}\le 4\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\]

A)                 There is a bounded solution       

B)                 There is no solution

C)                 There are infinite solutions

D)                 None of these

Correct Answer: C

Solution :

                As there may be infinite values of \[{{x}_{1}}\] and \[{{x}_{2}}\] on line\[{{x}_{1}}+{{x}_{2}}=1\].