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Linear Programming - ETEA Model Test MCQS - Part - I

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  • Linear Programming - ETEA Model Test MCQS - Part - I

    For the following shaded area, the linear constraints except $x\ge 0$ and $y\ge 0$ , are
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    $2x+y\le 2,\ x-y\le 1,\ x+2y\le 8$
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    $2x+y\ge 2,\ x-y\le 1,\ x+2y\le 8$
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    $2x+y\ge 2,\ x-y\ge 1,\ x+2y\le 8$
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    $2x+y\ge 2,\ x-y\ge 1,\ x+2y\ge 8$
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  • #2
    In equations $3x-y\ge 3$ and $4x-y>4$
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    Have solution for positive x and y
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    Have no solution for positive x and y
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    Have solution for all x
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    Have solution for all y
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    • #3
      Shaded region is represented by
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      $4x-2y\le 3$
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      $4x-2y\le -3$
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      $4x-2y\ge 3$
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      $4x-2y\ge -3$
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      • #4
        A Firm makes pents and shirts. A shirt takes 2 hour on machine and 3 hour of man labour while a pent takes 3 hour on machine and 2 hour of man labour. In a week there are 70 hour machine and 75 hour of man labour available. If the firm determine to make x shirts and y pents per week, then for this the linear constraints are
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        $x\ge 0,\ y\ge 0,\ 2x+3y\ge 70,\ 3x+2y\ge 75$
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        $x\ge 0,\ y\ge 0,\ 2x+3y\le 70,\ 3x+2y\ge 75$
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        $x\ge 0,\ y\ge 0,\ 2x+3y\ge 70,\ 3x+2y\le 75$
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        $x\ge 0,\ y\ge 0,\ 2x+3y\le 70,\ 3x+2y\le 75$
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        • #5
          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 ${{x}_{1}},\ {{x}_{2}}\ge 0$
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          ${{x}_{1}}=1.2$
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          ${{x}_{2}}=2.6$
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          $z=10.2$
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          All the above
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          • #6
            A company manufactures two types of products A and B. The storage capacity of its godown is 100 units. Total investment amount is Rs. 30,000. The cost price of A and B are Rs. 400 and Rs. 900 respectively. If all the products have sold and per unit profit is Rs. 100 and Rs. 120 through A and B respectively. If x units of A and y units of B be produced, then two linear constraints and iso-profit line are respectively
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            $x+y=100;\ 4x+9y=300,\ 100x+120y=c$
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            $x+y\le 100;\ 4x+9y\le 300,\ x+2y=c$
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            $x+y\le 100;\ 4x+9y\le 300,\ 100x+120y=c$
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            $x+y\le 100;\ 9x+4y\le 300,\ x+2y=c$
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            • #7
              The L.P. problem Max $z={{x}_{1}}+{{x}_{2}}$ such that $-2{{x}_{1}}+{{x}_{2}}\le 1,\ {{x}_{1}}\le 2,\ {{x}_{1}}+{{x}_{2}}\le 3$ and ${{x}_{1}},\ {{x}_{2}}\ge 0$ has
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              One solution
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              Three solution
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              An infinite no. of solution
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              None of these
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              • #8
                The minimum value of the objective function $z=2x+10y$ for linear constraints $x\ge 0,\ y\ge 0$ , $x-y\ge 0$ , $x-5y\le -5$ , is
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                10
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                15
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                12
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                8
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                • #9
                  The maximum value of $z=4x+3y$ subject to the constraints $3x+2y\ge 160,\ 5x+2y\ge 200$ , $x+2y\ge 80$ ; $x,\ y\ge 0$ is
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                  320
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                  300
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                  230
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                  None of these
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                  • #10
                    Minimize $z=\sum\limits_{j=1}^{n}{{}}\sum\limits_{i=1}^{m}{ {{c}_{ij}}\,{{x}_{ij}}}$ Subject to : $\sum\limits_{j=1}^{n}{{{x}_{ij}}\le {{a}_{i}},\ i=1,.......,m}$ $\sum\limits_{i=1}^{m}{{{x}_{ij}}={{b}_{j}},\ j=1,......,n}$ is a (L.P.P.) with number of constraints
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                    $m+n$
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                    $m-n$
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                    mn
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                    $\frac{m}{n}$
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