CBSE Questions for Class 12 Commerce Maths Linear Programming Quiz 5 - MCQExams.com

The shape of the region determined by $$ 2x+6y \geq 12, 3x +2y \geq 6, x+y \leq 8, x \geq 0, y \geq 0$$
  • a triangle
  • a quadrilateral
  • a pentagon
  • a hexagon
A_____ in a table represents a relationship among a set of values.
  • Column
  • Key
  • Row
  • Entry
The feasible region of an LPP is shown in the figure. If $$z=3x+9y$$, then the minimum value of z occurs at?
1623192_cdf6c666f0f44c088383682feeedacfe.PNG
  • $$(5, 5)$$
  • $$(0, 10)$$
  • $$(0, 20)$$
  • $$(15, 15)$$
For the LPP; maximise $$z=x+4y$$ subject to the constraints $$x+2y\leq 2$$, $$x+2y\geq 8$$, $$x, y\geq 0$$.
  • $$z_{max}=4$$
  • $$z_{max}=8$$
  • $$z_{max}=16$$
  • Has no feasible solution
If $$ 2x - y +1 = 0 $$ is tangent to the hyperbola $$ \frac {x^2}{a^2} - \frac {y^2}{16} = 1 $$ then which of the following CANNOT be sides of a right angled triangle?
  • a,4,1
  • 2a,4,1
  • a,4,2
  • 2a,8,1
Convex set: A set of point in a plane is said to be convex set it the line segment joining any two points in the set, completely lies in the set.
Which of the following sets represent the convex sets ? jistify your answer.
The minimum value of $$z=10x+25y$$ subject to $$0\leq x\leq 3, 0\leq y\leq 3, x+y\geq 5$$ is?
  • $$80$$
  • $$95$$
  • $$105$$
  • $$30$$
The maximum value of $$z=9x+11y$$ subject to $$3x+2y\leq 12, 2x+3y\leq 12$$, $$x\geq 0, y\geq 0$$ is _________.
  • $$44$$
  • $$54$$
  • $$36$$
  • $$48$$
Two towns A and B are 60 km  apart. A school is to built to serve 150 students in town A and 50 students in town B. If the total distance to be travelled by all 200 students is to be as small as possible, then the school be built at              
  • town B
  • 45 km from town A
  • town A
  • 45 km from town B
The feasible solution for a LPP is shown in Fig. Let $$Z = 3x - 4y$$ be the 
Objective function, Minimum of Z occurs at
1799578_06b2877c69cf41f4a6b3c0f2d4fede1c.png
  • (0, 0)
  • (0, 8)
  • (0, 5)
  • (4, 10)
The feasible solution for a LPP is shown in Fig. Let Z=3x−4y be the 
The objective function, Maximum value of Z + Minimum value of Z is equal to 
1799590_c9608e2be9eb4172a7eef4c31185c93f.PNG
  • 13
  • 1
  • -13
  • -17
The feasible solution for a LPP is shown in Fig. Let Z=3x−4y be the 
Objective function, Maximum of Z occurs at

1799584_7d02553c3e704951a2531cdd27e30e79.PNG
  • (5, 0)
  • (6, 5)
  • (6, 8)
  • (4, 10)
The corner points of the feasible region determined by the system of linear constraints are (0, 0), (o, 40), (20, 40), (60, 20), (60, 0). The objective function is $$Z = 4x + 3y$$.
Compare the quantity in Column A and Column B
1799565_061212ee7da54ea09892dcd6f25cda30.png
  • The quantity in column A is greater
  • The quantity in column B is greater
  • The two quantities are equal
  • The relationship cannot be determined on the basis of the information Supplied
State true or false. 
In a LPP, the minimum value of the objective function Z = ax + by is always 0 if origin is one of the corner point of the feasible region.
  • True
  • False
State true or false.
If the feasible region for a LPP is unbounded, maximum or minimum of the objective function Z = ax + by may or may not exist.
  • True
  • False
State true or false. 
In a LPP, the maximum value of the objective function Z = ax + by is always finite.
  • True
  • False
State true or false. 
Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.
  • True
  • False
The value of objective function is maximum under linear constraints
  • at the centre of feasible region
  • at (0,0)
  • at the vertex of feasible region
  • the vertex which is of maximum distance from (0,0)
Of all the points of the feasible region, the optimal value of z obtained at the point lies
  • inside the feasible region
  • at the boundary of the feasible region
  • at vertex of feasible region
  • outside the feasible region

Object function of LPP is
  • a constraint
  • a function to be maximized or minimized
  • a relation between the decision variables
  • equation of a straight line
The corner points of the feasible solution given by the inequation $$x + y \leq 4, 2x + y \leq 7, x \geq 0, y \geq 0$$ are
  • (0 ,0), (4, 0), (7, 1), (0, 4)
  • (0, 0), $$(\dfrac{7}{2}, 0)$$, (3, 1), (0, 4)
  • (0, 0), $$(\dfrac{7}{2}, 0)$$, (3, 1), (0, 7)
  • (0, 0), (4, 0), (3, 1), (0, &)
Solution of LPP to minimize z = 2x + 3y, such that $$x \geq 0, y \geq 0, 1 \leq x + 2y  \leq 10 $$ is
  • $$x = 0, y = \dfrac{1}{2}$$
  • $$x = \dfrac{1}{2}, y = 0$$
  • $$x = 1, y = 2$$
  • $$x = \dfrac{1}{2}, y = \dfrac{1}{2}$$
Find the output of the program given below if$$ x = 48$$
and $$y = 60$$
10  $$ READ x, y$$
20  $$Let x = x/3$$
30  $$ Let y = x + y + 8$$
40  $$ z = \dfrac y4$$
50  $$PRINT z$$
60  $$End$$
  • $$21$$
  • $$22$$
  • $$23$$
  • $$24$$
10 students of class X took part in a Mathematics quiz If the number of girls is 4 more than the number of boys find the number of boys and girls who took part in the quiz Which graph represents the solution of the problem?
A retired person wants to invest an amount of Rs. $$50, 000.$$ His broker recommends investing in two type of bonds A and B yielding $$10 \%$$ and $$9 \%$$ return respectively on the invested amount. He decides to invest at least $$Rs. 20,000$$ in bond A and at least $$Rs. \ 10,000$$ in bond B. He also wants to invest at least as much in bond A as in bond B. Solve this linear programming problem graphically to maximize his returns.
  • $$4900$$
  • $$2900$$
  • $$5400$$
  • $$4000$$
A manufacturer produces nuts and bolts. It takes $$1$$ hour of work on machine A and $$3$$ hours on machine B to produce a package of nuts. It takes $$3$$ hours on machine A and $$1$$ hour on machine B to produce a package of bolts. He earns a profit of $$Rs. 17.50$$ per package on nuts and $$Rs 7$$ per package of bolts. How many packages of each should be produced each day so as to maximize his profits if he operate his machines for at the most $$12$$ hours a day? 
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
Conclude from the following:
$$n^2 > 10$$, and n is a positive integer.
A: $$n^3$$
B: $$50$$
  • The quantity A is may be greater or smaller than B.
  • The quantity B is greater than A.
  • The two quantities are equal.
  • The relationship cannot be determined from the information given.
If  $$\displaystyle x\ge 0$$
$$\displaystyle 3y-2x\ge -12$$
$$\displaystyle 2x+5y\le 20$$
The area of the triangle formed in the xy plane by the system of inequalities above is:
  • $$60$$
  • $$30$$
  • $$40$$
  • $$50$$
Minimize : $$z=3x+y$$, subject to $$2x+3y\le 6, x+y \ge 1, x\ge 0, y\ge 0$$
  • $$x=1, y=1$$
  • $$x=0, y=1$$
  • $$x=1, y=0$$
  • $$x=-1, y=-1$$
A manufacturer considers that men and women workers are equally efficient and so he pays them at the same rate. He has $$30$$ workers (male and female) and $$17$$ units capital; which he uses to produce two types of goods $$A$$ and $$B$$. To produce one unit of $$A$$, $$2$$ workers and $$3$$ units of capital are required while $$3$$ workers and $$1$$ unit of capital is required to produce one unit of $$B$$. If $$A$$ and $$B$$ are priced at $$Rs.\  100$$ and $$Rs.\ 120$$ per unit respectively, how should he use his resources to maximise the total revenue? Form the LPP and solve graphically.
Do you agree with this view of the manufacturer that men and women workers are equally efficient and so should be paid at the same rate?
  • $$1260$$
  • $$1130$$
  • $$1290$$
  • $$3421$$
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Practice Class 12 Commerce Maths Quiz Questions and Answers