question_answer

The minimum value of\[z=2{{x}_{1}}+3{{x}_{2}}\] subject to the constraints\[2{{x}_{1}}+7{{x}_{2}}\ge 22\],\[{{x}_{1}}+{{x}_{2}}\ge 6\],\[5{{x}_{1}}+{{x}_{2}}\ge 10\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\] is              [MP PET 2003]

A)                 14          

B)                 20

C)                 10          

D)                 16

Correct Answer: A

Solution :

                Obviously, at point (4, 2), the minimum value of \[z=2{{x}_{1}}+3{{x}_{2}}=2(4)+3(2)=14\].