JEE Main & Advanced Mathematics Linear Programming Question Bank Critical Thinking

  • question_answer For the following shaded area, the linear constraints except \[x\ge 0\] and \[y\ge 0\], are   

    A)                 \[2x+y\le 2,\ x-y\le 1,\ x+2y\le 8\]          

    B)                 \[2x+y\ge 2,\ x-y\le 1,\ x+2y\le 8\]

    C)                 \[2x+y\ge 2,\ x-y\ge 1,\ x+2y\le 8\]        

    D)                 \[2x+y\ge 2,\ x-y\ge 1,\ x+2y\ge 8\]

    Correct Answer: B

    Solution :

     To test the origin for \[2x+y=2,x-y=1\] and \[x+2y=8\]in reference to shaded area, \[0+0<2\]is true for \[2x+y=2\].  So for the region does not include origin (0, 0), \[2x+y\ge 2\]. Again for \[x-y=1,\,0-0<1\], \[\therefore \,\,\,\,x-y\le 1\] Similarly for \[x+2y=8,0+0<8\];  \ \[x+2y\le 8\].

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