question_answer

By graphical method, the solution of linear programming problem Maximize \[z=3{{x}_{1}}+5{{x}_{2}}\] Subject to \[3{{x}_{1}}+2{{x}_{2}}\le 18\], \[{{x}_{1}}\le 4\], \[{{x}_{2}}\le 6\],\[{{x}_{1}}\ge 0\],\[{{x}_{2}}\ge 0\] is             [MP PET 1996]

A)                 \[{{x}_{1}}=2,\ {{x}_{2}}=0,\ z=6\]           

B)                 \[{{x}_{1}}=2,\ {{x}_{2}}=6,\ z=36\]

C)                 \[{{x}_{1}}=4,\ {{x}_{2}}=3,\ z=27\]         

D)                 \[{{x}_{1}}=4,\ {{x}_{2}}=6,\ z=42\]

Correct Answer: B

Solution :

                Here feasible region has vertices (0, 0); (4, 0); (4, 3);  (2, 6) and (0, 6).                 \Max z at \[(2,\,6)=3(2)+5(6)=36\].