CBSE Questions for Class 12 Commerce Maths Linear Programming Quiz 1 - MCQExams.com

Minimise $$Z=\sum _{ j=1 }^{ n }{ \sum _{ i=1 }^{ m }{ { c }_{ ij }.{ x }_{ ij } }  } $$
Subject to $$\sum _{ i=1 }^{ m }{ { x }_{ ij } } ={ b }_{ j },j=1,2,......n$$
$$\sum _{ j=1 }^{ n }{ { x }_{ ij } } ={ b }_{ j },j=1,2,......,m$$ is a LPP with number of constraints
  • $$m-n$$
  • $$mn$$
  • $$m+n$$
  • $$\cfrac { m }{ n } $$
The solution of the set of constraints of a linear programming problem is a convex (open or closed) is called ______ region.
  • feasible
  • active
  • linear
  • none of these
Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using simplex), we find that
  • The values of decision variables obtained by rounding off are always very close to the optimal values.
  • The value of the objective function for a maximization problem will likely be less than that for the simplex solution.
  • The value of the objective function for a minimization problem will likely be less than that for the simplex solution.
  • All constraints are satisfied exactly.
  • None of the above.
If a = b then ax = ...........
  • $$b + x$$
  • bx
  • b - x
  • $$b\, \div\, x$$
The bar graph shows the grades obtained by a group of pupils in a test.
If grade C is the passing mark, how many pupils passed the test?

407807_3f3eaf2b94e44e8b8e7a4309fee6bd7f.png
  • 10
  • 14
  • 24
  • 30
An iso-profit line represents
  • An infinite number of solutions all of which yield the same profit
  • An infinite number of solution all of which yield the same cost
  • An infinite number of optimal solutions
  • A boundary of the feasible region
In linear programming, lack of points for a solution set is said to
  • have no feasible solution
  • have a feasible solution
  • have single point method
  • have infinte point method
If  x + y = 3 and xy = 2, then the value of $$\displaystyle x^{3}-y^{3}$$ is equal to 
  • 6
  • 7
  • 8
  • 0
If the constraints in linear programming problem are changed
  • the problem is to be re-evaluated
  • solution is not defined
  • the objective function has to be modified
  • the change in constraints is ignored
The bar graph shows the number of cakes sold at a shop in four days.
What is the difference in number of cakes between the highest and the lowest daily sale?

407804_a50f8fd2015f46a7986020a56d31adcb.png
  • 20
  • 35
  • 30
  • 40

Objective of linear programming for an objective function is to
    • maximize or minimize.
    • subset or proper set modeling.
    • row or column modeling.
    • adjacent modeling.
    If the feasible region for a solution of linear inequations is bounded, it is called as:
    • Concave Polygon
    • Finite Region
    • Convex Polygon
    • None of the above
    If an iso-profit line yielding the optimal solution coincides with a constaint line, then
    • The solution is unbounded
    • The solution is infeasible
    • The constraint which coincides is redundant
    • None of the above
    Graphical method can be used only when the decision variables is
    • more than 3.
    • more than 1.
    • Two
    • one
    Objective of LPP is
    • A constraint
    • A function to be optimized
    • A relation between the variables
    • None of the above
    The shaded part of a given figure indicates the feasible region, then the constraints are
    633855_cdc9ead073ef4bd480766c35456467fd.png
    • $$x,y\ge 0,x+y\ge 0,x\ge 5,y\le 3$$
    • $$x,y\ge 0,x-y\ge 0,x\le 5,y\le 3\quad $$
    • $$x,y\ge 0,x-y\ge 0,x\le 5,y\ge 3$$
    • $$x,y\ge 0,x-y\le 0,x\le 5,y\le 3$$
    The feasible solution of an LP problem, is ________
    • must satisfies all of the problem's constraints simultaneously
    • must be a corner point of the feasible region
    • need not satisfy all of the constraints, only some of them
    • must optimize the value of the objective function
    The corner points of the feasible region determined by the system of linear constraints are $$(0, 10),(5, 5), (25, 20)$$ and $$(0, 30)$$. Let $$Z = px + qy$$, where $$p, q > 0$$. Condition on $$p$$ and $$q$$ so that the maximum of $$Z$$ occurs at both the points $$(25, 20)$$ and $$(0, 30)$$ is _______.
    • $$5p = 2q$$
    • $$2p = 5q$$
    • $$p = 2q$$
    • $$q = 3p$$
    The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.
     Colour   Number of cars manufactured
     Vento CretaWagonR 
     Red 65 88 93
     White 54 42 80
     Black 66 52 88
     Sliver37 49 74
    What was the total number of black cars manufactured?
    • $$240$$
    • $$206$$
    • $$205$$
    • $$159$$
    The taxi fare in a city is as follows: For the first kilometre, the fare is Rs. $$8$$ and the subsequent distance it is Rs. $$5$$ per km. Taking the distance covered as x km and fare as Rs y, write a linear equation.
    • $$y=4+6x$$
    • $$y=3+5x$$
    • $$y=4+5x$$
    • $$y=3+6x$$
    The number of points in $$\\ \left( -\infty ,\infty  \right) $$ for which $${ x }^{ 2 }-x\sin { x } -\cos { x } =0$$, is
    • $$6$$
    • $$4$$
    • $$2$$
    • None of the above
    Minimize: $$z=\sum _{ j=1 }^{ n }{ \sum _{ i=1 }^{ m }{ { c }_{ ij }.{ x }_{ ij } }  } $$
    subject to : $$\sum _{ j=1 }^{ n }{ { x }_{ ij }={ a }_{ i } } ,i=1,....m;\quad \sum _{ i=1 }^{ m }{ { x }_{ ij }={ b }_{ j } } ,j=1,....n$$ is a LPP with number of constraints
    • $$m+n$$
    • $$m0n$$
    • $$mn$$
    • $$\cfrac{m}{n}$$
    What is the solution of $$x\le 4,y\ge 0$$ and $$x\le -4,y\le 0$$ ?
    • $$x\ge -4,y\le 0$$
    • $$x\le 4,y\ge 0$$
    • $$x\le -4,y=0$$
    • $$x\ge -4,y=0$$

    A graph is shown, state whether it is a function ?
    State true or false

    99772_ba827a90813e4edbb62bd5f062eb206f.png
    • True
    • False
    The ratio of the rate of flow of water in pipes varies inversely as the square of the radius of the pipes. What is the ratio of the rates of flow in two pipes diameters 2 cm and 4 cm?
    • 1 : 6
    • 1 : 4
    • 1 : 2
    • 3 : 1
    The diagram shows a scale drawing of a garden which is p metre long and w metre wide.
    (a) Write an inequality between p and w.
    (b) If a path of 2 m width is added to two sides as shown in the diagram, write a new inequality between the length and the width.
    104974_e52fdf50efdd4b6883958f2565b98e8a.png
    • (a) $$p < w$$
      (b) $$p+2 > w+2$$
    • (a) $$p > w$$
      (b) $$p+2 >w+2$$
    • Data insufficient
    • None of these
    If $$A=$${1,2,3};$$   B=$$ {3,4,5};$$ C=$${4,6}, then $$A\times (B\cap C)=?$$
    • {(2,4)(1,4)}
    • {(2,4)(3,4)(5,6)}
    • {(1,4)(2,4)(3,4)}
    • None of these
    The value of $$\displaystyle \frac{0.76\times0.76\times0.76+0.24\times0.24\times0.24 }{0.76\times0.76-0.76\times0.24+0.24\times0.24}$$ is 
    • 0.52
    • 1
    • 0.01
    • 0.1
    The incomplete graph shows Dinesh's savings from January to April.
    Dinesh saved a total of RS. 730 during the four months. The amount of money saved in February was as much as that saved in March. How much did he save in March?

    407806_637eecf21a1d452ab76d0e29c35c67dd.png
    • Rs. 245
    • Rs. 275
    • Rs. 250
    • Rs. 295
    ?
    393682_be07a13ce02e4d8cba592d42d841be22.png
    • $$212$$
    • $$532$$
    • $$244$$
    • $$733$$
    0:0:1


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