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Linear Programming - ETEA Model Test MCQS - Part - V

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

    The constraints $-{{x}_{1}}+{{x}_{2}}\le 1$ $-{{x}_{1}}+3{{x}_{2}}\le 9$ ${{x}_{1}},\ {{x}_{2}}\ \ge 0$ define on
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    Bounded feasible space
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    Unbounded feasible space
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    Both bounded and unbounded feasible space
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    None of these
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  • #2
    Which of the following is not true for linear programming problems
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    A slack variable is a variable added to the left hand side of a less than or equal to constraint to convert it into an equality
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    A surplus variable is a variable subtracted from the left hand side of a greater than or equal to constraint to convert it into an equality
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    A basic solution which is also in the feasible region is called a basic feasible solution
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    A column in the simplex tableau that contains all of the variables in the solution is called pivot or key column
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    • #3
      Which of the terms is not used in a linear programming problem
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      Slack variables
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      Objective function
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      Concave region
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      Feasible solution
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      • #4
        The graph of inequations $x\le y$ and $y\le x+3$ is located in
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        II quadrant
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        I, II quadrants
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        I, II, III quadrants
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        II, III, IV quadrants
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        • #5
          The area of the feasible region for the following constraints $3y+x\ge 3,\,x\ge 0,\,y\ge 0$ will be
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          Bounded
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          Unbounded
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          Convex
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          Concave
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          • #6
            The feasible region for the following constraints ${{L}_{1}}\le 0,{{L}_{2}}\ge 0,\,{{L}_{3}}=0,\,x\ge 0,y\ge 0$ in the diagram shown is
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            Area DHF
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            Area AHC
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            Line segment EG
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            Line segment GI
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            • #7
              A wholesale merchant wants to start the business of cereal with Rs. 24000. Wheat is Rs. 400 per quintal and rice is Rs. 600 per quintal. He has capacity to store 200 quintal cereal. He earns the profit Rs. 25 per quintal on wheat and Rs. 40 per quintal on rice. If he stores x quintal rice and y quintal wheat, then for maximum profit the objective function is
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              $25x+40y$
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              $40x+25y$
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              $400x+600y$
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              $\frac{400}{40}x+\frac{600}{25}y$
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              • #8
                Mohan wants to invest the total amount of Rs. 15,000 in saving certificates and national saving bonds. According to rules, he has to invest at least Rs. 2000 in saving certificates and Rs. 2500 in national saving bonds. The interest rate is 8% on saving certificate and 10% on national saving bonds per annum. He invest Rs. x in saving certificates and Rs. y in national saving bonds. Then the objective function for this problem is
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                $\0.08x+0.10y$
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                $\frac{x}{2000}+\frac{y}{2500}$
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                $2000x+2500y$
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                $\frac{x}{8}+\frac{y}{10}$
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                • #9
                  A firm produces two types of products A and B. The profit on both is Rs. 2 per item. Every product requires processing on machines ${{M}_{1}}$ and ${{M}_{2}}$ . For A, machines ${{M}_{1}}$ and ${{M}_{2}}$ takes 1 minute and 2 minute respectively and for B, machines ${{M}_{1}}$ and ${{M}_{2}}$ takes the time 1 minute each. The machines ${{M}_{1}},\ {{M}_{2}}$ are not available more than 8 hours and 10 hours, any of day, respectively. If the products made x of A and y of B, then the linear constraints for the L.P.P. except $x\ge 0,\ y\ge 0$ , are
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                  $x+y\le 480\,,\ 2x+y\le 600$
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                  $x+y\le 8,\ 2x+y\le 10$
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                  $x+y\ge 480\,,\ 2x+y\ge 600$
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                  $x+y\le 8,\ 2x+y\ge 10$
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                  • #10
                    The objective function in the above question is
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                    $2x+y$
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                    $x+2y$
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                    $2x+2y$
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                    $8x+10y$
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