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JEE Main & Advanced Mathematics Linear Programming Question Bank Self Evaluation Test - Linear Programming

  • question_answer
    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

    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 :

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


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