JEE Main & Advanced Mathematics Linear Programming Question Bank Critical Thinking

  • question_answer For the L.P. problem Min\[z=2{{x}_{1}}+3{{x}_{2}}\] such that \[-{{x}_{1}}+2{{x}_{2}}\le 4,\] \[{{x}_{1}}+{{x}_{2}}\le 6,\ \ {{x}_{1}}+3{{x}_{2}}\ge 9\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\]

    A)                 \[{{x}_{1}}=1.2\]              

    B)                 \[{{x}_{2}}=2.6\]

    C)                 \[z=10.2\]           

    D)                 All the above

    Correct Answer: D

    Solution :

               The graph of linear programming problem is as given below            Hence the required feasible region is given by the graph whose vertices are\[A\,(1.2,\,2.6),B(4.5,\,1.5)\]and\[C\,\left( \frac{8}{3},\frac{10}{3} \right)\].                    Thus objective function is minimum at \[A\,(1.2,\,2.6)\]                                 So \[{{x}_{1}}=1.2,\,{{x}_{2}}=2.6\]and\[z=2\times 1.2+3\times 2.6=10.2\].

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