Download App

MATHS M.C.Q (1 Marks)

Linear Programming · Rajasthan Board (RBSE) STD 12 Science (Rajasthan - English Medium). 157 questions.

Questions · Page 1 of 4

M.C.Q (1 Marks)

🎯

Test yourself on this topic

50 questions · timed · auto-graded

MCQ 11 Mark
The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (4, 0), (2, 4) and (0, 5). If the maximum value of z = ax + by, where a, b > 0 occurs at both (2, 4) and (4, 0), then:
  • ✓
    a = 2b
  • B
    2a = b
  • C
    a = b
  • D
    3a = b
Answer
Correct option: A.
a = 2b
4a + 0b = 2a + 4b
4a = 2a + 4b
4a - 2a = 4b
2a = 4b
a = 2b
View full question & answer→
MCQ 21 Mark
The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (4, 0), (2, 4) and (0, 5). If the maximum value of z = ax + by, where a, b > 0 occurs at both (2, 4) and (4, 0), then:
  • ✓
    a = 2b
  • B
    2a = b
  • C
    a = b
  • D
    3a = b
Answer
Correct option: A.
a = 2b
4a + 0b = 2a + 4b
4a = 2a + 4b
4a - 2a = 4b
2a = 4b
a = 2b
View full question & answer→
MCQ 31 Mark
The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (4, 0), (2, 4) and (0, 5). If the maximum value of z = ax + by, where a, b > 0 occurs at both (2, 4) and (4, 0), then:
  • ✓
    a = 2b
  • B
    2a = b
  • C
    a = b
  • D
    3a = b
Answer
Correct option: A.
a = 2b
4a + 0b = 2a + 4b
4a = 2a + 4b
4a - 2a = 4b
2a = 4b
a = 2b
View full question & answer→
MCQ 41 Mark
Maximize $Z = 11x + 8y,$ subject to $\text{x}\leq4,\text{y}\leq6,\text{x}\geq0,\text{y}\geq0.$
  • A
    $\text{44 at (4, 2)}$
  • ✓
    $\text{60 at (4, 2)}$
  • C
    $\text{62 at (4, 0)}$
  • D
    None of these
Answer
Correct option: B.
$\text{60 at (4, 2)}$
View full question & answer→
MCQ 51 Mark
The corner point of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y. Compare the quantity in Column A and Column B.
Column A
Column B
Maximum of Z
325
  • A
    The quantity in column A is greater.
  • ✓
    The quantity in column B is greater.
  • C
    The two quantities are equal.
  • D
    The relationship cannot be determined On the basis of the information supplied.
Answer
Correct option: B.
The quantity in column B is greater.
The quantity in column B is greater.
View full question & answer→
MCQ 61 Mark
The value of $\frac{0.76\times0.76\times0.76+0.24\times0.24\times0.24}{0.76\times0.76-0.76\times0.24+ 0.24+0.24}$ is:
  • A
    $0.52$
  • ✓
    $1$
  • C
    $0.01$
  • D
    $0.1$
Answer
Correct option: B.
$1$
Formula used:
$a^3 + b^3= (a + b)(a^2 - ab + b^2)$
$\frac{0.76\times0.76\times0.76+0.24\times0.24\times0.24}{0.76\times0.76-0.76\times0.24+ 0.24+0.24}$
$\frac{(0.76)^{3}+(0.24)^{3}}{0.76\times0.76-0.76\times0.24+0.24+0.24}$
$=\frac{(0.76+0.24)(0.76\times0.76-0.76\times0.24+0.24\times0.24)}{0.76\times0.76-0.76\times0.24+0.24\times0.24}$
$=(0.76+0.24)=1$
View full question & answer→
MCQ 71 Mark
The maximum value of Z = 4x + 2y Subjected to the constraints $2\text{x}+3\text{y}\leq18,\text{x}+\text{y}\geq10,\text{x},\text{y}\geq0$ is:
  • A
    36
  • B
    40
  • C
    20
  • ✓
    none of these
Answer
Correct option: D.
none of these

Consider, 2x + 3y = 18

x
y
(x, y)
0
6
(0, 6)
9
0
(9, 0)
Consider, x + y = 10
x
y
(x, y)
0
10
(0, 10)
10
0
(10, 0)
From the graph we conclude that no feasible region exist.
View full question & answer→
MCQ 81 Mark
In transportation models designed in linear programming, points of demand is classified as:
  • A
    Ordination
  • B
    Transportation
  • ✓
    Destinations
  • D
    Origins
Answer
Correct option: C.
Destinations
In linear programming, transportation modeltransportation model are applied to problems related to the study of efficient transportation routes.
i.e., how effectively the available resources are transported to different destinations with minimum cost.
Therefore, the points of demand is classified as destinations.
View full question & answer→
MCQ 91 Mark
Objective function of a $\text{LPP}$ is:
  • A
    a constraint
  • ✓
    a function to be optimized
  • C
    a relation between the variables
  • D
    none of these
Answer
Correct option: B.
a function to be optimized
a function to be optimized
View full question & answer→
MCQ 101 Mark
The maximum value of Z = 4x + 3y subjected to the constraints 3x + 2y ≥ 160, 5x + 2y ≥ 200, x + 2y ≥ 80, x, y ≥ 0 is:
  • A
    320
  • B
    300
  • C
    230
  • ✓
    none of these
Answer
Correct option: D.
none of these
We need to maximize the function Z = 4x + 3y
Converting the given inequations into equations, we obtain
3x + 2y = 160, 5x + 2y = 200, x + 2y = 80, x = 0 and y = 0
Region represented by 3x + 2y ≥ 160:
The line 3x + 2y = 160 meets the coordinate axes at A1603,0 and B(0, 80) respectively.
By joining these points we obtain the line 3x + 2y = 160.
Clearly (0, 0) does not satisfies the inequation 3x + 2y ≥ 160.
So, the region in xy plane which does not contain the origin represents the solution set of the inequation 3x + 2y ≥ 160.
Region represented by 5x +2y ≥ 200:
The line 5x + 2y = 200 meets the coordinate axes at C(40, 0) and D(0, 100) respectively.
By joining these points we obtain the line 5x + 2y = 200.
Clearly (0, 0) does not satisfies the inequation 5x +2y ≥ 200.
So, the region which does not contain the origin represents the solution set of the inequation 5x +2y ≥ 200.
Region represented by x +2y ≥ 80:
The line x + 2y = 80 meets the coordinate axes at E(80, 0) and F(0, 40) respectively.
By joining these points we obtain the line x + 2y = 80.
Clearly (0, 0) does not satisfies the inequation x + 2y ≥ 80.
So, the region which does not contain the origin represents the solution set of the inequation x + 2y ≥ 80.
Region represented by x ≥ 0 and y ≥ 0:
Since, every point in the first quadrant satisfies these inequations.
So, the first quadrant is the region represented by the inequations x ≥ 0, and y ≥ 0.
The feasible region determined by the system of constraints 3x + 2y ≥ 160,5x+2y ≥ 200, x +2y ≥ 80, x ≥ 0, and y ≥ 0 are as follows.

Here, we see that the feasible region is unbounded.
Therefore,maximum value is infinity.
View full question & answer→
MCQ 111 Mark
Graphical method can be used only when the decision variables is:
  • A
    More than 3.
  • B
    More than 1.
  • ✓
    Two
  • D
    One
Answer
Correct option: C.
Two
Graphical method can be used only when the decision variables is two.
View full question & answer→
MCQ 121 Mark
A constraint in an LP model becomes redundant because:
  • A
    Two iso - profit line may be parallel to each other
  • B
    The solution is unbounded
  • C
    This constraint is not satisfied by the solution values
  • ✓
    None of the above
Answer
Correct option: D.
None of the above
A constraint in an LP model becomes redundant when the feasible region doesnt change by the removing the constraint.
For example, $\text{x}+2\text{y}\leq20$ and $2\text{x}+4\text{y}\leq40$ are the constraints.
$2\text{x}+4\text{y}\leq40$
$\Rightarrow2\times(\text{x}+2\text{y})\leq2\times20$
$\Rightarrow\text{x}+2\text{y}\leq20$
which is same as the first constraint.
Therefore, $2\text{x}+4\text{y}\leq40$ can be removed.
By removing this constraint feasible region doesnt change.
View full question & answer→
MCQ 131 Mark
Maximize Z = 3x + 5y, subject to constraints: $\text{x}+4\text{y}\leq24,3\text{x}+\text{y}\leq21,\text{x}+\text{y}\geq9,\text{x}\geq0,\text{y}\geq0.$
  • A
    20 at (1, 0)
  • B
    30 at (0, 6)
  • ✓
    37 at (4, 5)
  • D
    33 at (6, 3)
Answer
Correct option: C.
37 at (4, 5)
Find the maximum value of Z = 3x + 5y referring to the explanation of Q.5.
View full question & answer→
MCQ 141 Mark
An objective function in a linear program can be which of the following?
  • ✓
    A maximization function
  • B
    A nonlinear maximization function
  • C
    A quadratic maximization function
  • D
    An uncertain quantity
Answer
Correct option: A.
A maximization function
Linear programming problem may be defined as the problem of maximizing or minimizing a linear function subject to linear constraints.
The objective function in a linear program is a maximization function.
View full question & answer→
MCQ 151 Mark
The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.
 
Number of cars manufactured
Colour
Vento
Creta
Wagonr
Red
65
88
93
White
54
42
80
Black
66
52
88
Sliver
37
49
74
Which car was twice the number of silver Vento?
  • ✓
    Silver WagonR
  • B
    Red WagonR
  • C
    Red Vento
  • D
    White Creta
Answer
Correct option: A.
Silver WagonR
The number of silver Vento car = 37 (from the table)
Twice the number of silver Vento cars = 2 × 37 = 74
Now from table we can see that silver WagonR is only car type having 74 cars
View full question & answer→
MCQ 161 Mark
The corner points of the feasible region determined by the following system of linear inequalities:
2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5).
Let Z = px + qy, where p.q > 0.
Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is:
  • A
    P = q
  • B
    p = 2q
  • C
    p = 3q
  • ✓
    q = 3q
Answer
Correct option: D.
q = 3q
The maximum value of Z is unique.
It is given that the maximum value of Z occurs at two points (3, 4) and (0,5).
Value of Z at (3, 4) = Value of Z at (0,5)
= p(3) + q(4) = p(0) + 7(5)
= 3p + 4q = 5q
= q = 3p
View full question & answer→
MCQ 171 Mark
The objective function Z = 4x + 3y can be maximised subjected to the constraints 3x + 4y ≤ 24, 8x + 6y ≤ 48, x ≤ 5, y ≤ 6, x, y ≥ 0
  • A
    at only one point
  • B
    at two points only
  • ✓
    at an infinite number of points
  • D
    none of these
Answer
Correct option: C.
at an infinite number of points
We need to maximize Z = 4x + 3y
First, we will convert the given inequations into equations, we obtain the following equations: 3x + 4y = 24, 8x + 6y = 48, x = 5, y = 6, x = 0 and y = 0.
The line 3x + 4y = 24 meets the coordinate axis at A(8, 0) and B(0, 6).
Join these points to obtain the line 3x + 4y = 24.
Clearly, (0, 0) satisfies the inequation 3x + 4y ≤ 24.
So, the region in xy-plane that contains the origin represents the solution set of the given equation.
The line 8x + 6y = 48 meets the coordinate axis at C(6, 0) and D(0, 8).
Join these points to obtain the line 8x + 6y = 48.
Clearly, (0, 0) satisfies the inequation 8x + 6y ≤ 48.
So, the region in xy plane that contains the origin represents the solution set of the given equation.
x = 5 is the line passing through x = 5 parallel to the Y axis.
y = 6 is the line passing through y = 6 parallel to the X axis.
Region represented by x ≥ 0 and y ≥ 0:
Since, every point in the first quadrant satisfies these inequations.
So, the first quadrant is the region represented by the inequations.
These lines are drawn using a suitable scale.
and B (0,6).
The corner points of the feasible region are O(0, 0), G(5, 0), $\text{F}\Big(5,\frac{4}{3}\Big),\text{E}\Big(\frac{24}{7},\frac{24}{7}\Big)$and B(0, 6).
The values of Z at these corner points are as follows.
$\text{Corner point}$ $\text{Z} = 4\text{x} + 3\text{y}$
$\text{O}(0, 0)$ $4 \times 0 + 3 \times 0= 0$
$\text{G}(5, 0)$ $4 \times 5 + 3 \times 0 = 20$
$\text{F}\Big(5,\frac{4}{3}\Big)$ $4\times5+3\times\frac{4}{3}=24$
$\text{E}\Big(\frac{24}{7},\frac{24}{7}\Big)$ $4\times\frac{24}{7}+3\times\frac{24}{7}=\frac{196}{7}=24$
$\text{B}(0, 6)$ $4\times0+3\times6=18$
We see that the maximum value of the objective function Z is 24 which is at F(5, 4) and $\text{E}\Big(\frac{24}{7},\frac{24}{7}\Big).$
Thus, the optimal value of Z is 24.
As, we know that if a LPP has two optimal solution, then there are an infinite number of optimal solutions.
Therefore, the given objective function can be subjected at an infinite number of points.
View full question & answer→
MCQ 181 Mark
The corner points of the feasible region determined by the following system of linear inequalities:
$2\text{x}+\text{y}\le10,\ \text{x}+3\text{y}\le15,\ \text{x},\ \text{y}\ge0$ are (0, 0), (5, 0), (3, 4) and (0, 5). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is:
  • A
    p = q
  • B
    p = 2q
  • C
    p = 3q
  • ✓
    q = 3p.
Answer
Correct option: D.
q = 3p.
The maximum value of Z is unique.
It is given that the maximum value of Z occurs at two points, (3, 4) and (0, 5).
$\therefore$ Value of z at (3, 4) = Value of z at (0, 5)
⇒ p(3) + q(4) = p(0) + q(5)
⇒ 3p + 4q = 5q
⇒ q = 3p
Hence, the correct answer is D.
View full question & answer→
MCQ 191 Mark
In an LPP, if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then the number of points of which Zmax occurs is:
  • A
    0
  • B
    2
  • C
    Finite
  • ✓
    Infinite
Answer
Correct option: D.
Infinite
Infinite
View full question & answer→
MCQ 201 Mark
A linear programming of linear functions deals with:
  • A
    Minimizing
  • ✓
    Optimizing
  • C
    Maximizing
  • D
    None
Answer
Correct option: B.
Optimizing
Optimizing
View full question & answer→
MCQ 211 Mark
Maximize Z = 4x + 6y, subject to $3\text{x}+2\text{y}\leq12,\text{x}+\text{y}\geq4,\text{x},\text{y}\geq0.$
  • A
    16 at (4, 0)
  • B
    24 at (0, 4)
  • C
    24 at (6, 0)
  • ✓
    36 at (0, 6)
Answer
Correct option: D.
36 at (0, 6)
36 at (0, 6)
View full question & answer→
MCQ 221 Mark
The __________ is the method available for solving an L.P.P
  • ✓
    Graphical method
  • B
    Least cost method
  • C
    MODI method
  • D
    Hungarian method
Answer
Correct option: A.
Graphical method
There are different methods to solve an linear programming problem.
Such as Graphical method, Simplex method, Ellipsoid method, Interior point methods.
View full question & answer→
MCQ 231 Mark
Linear programming model which involves funds allocation of limited investment is classified as:
  • A
    Ordination budgeting model
  • ✓
    Capital budgeting models
  • C
    Funds investment models
  • D
    Funds origin models
Answer
Correct option: B.
Capital budgeting models
In linear programming, Capital budgeting models to minimize the total capital cost.
The solutions from the model are used to decide the best combination of capital resources and best times to start and finish projects and to determine the net capital cost.
View full question & answer→
MCQ 241 Mark
The problem associated with LPP is:
  • ✓
    Single objective function
  • B
    Double objective function
  • C
    No any objective function
  • D
    None
Answer
Correct option: A.
Single objective function
The problem associated with LLP is single objective.
View full question & answer→
MCQ 251 Mark
Choose the correct answer from the given four options.

The feasible solution for a LPP shown in Fig. 12.12. Let z = 3x - 4y be objective functio. (Maximum value of Z + Minimum value of Z) is equal to:
  • A
    13.
  • B
    1.
  • C
    -13.
  • ✓
    -17.
Answer
Correct option: D.
-17.
 
Corner points
Corresponding value of Z = 3x - 4y
(0, 0)
(5, 0)
(6, 5)
(6, 8)
(4, 10)
(0, 8)
0
15 (Maximum)
-2
-14
-28
-32 (Minimum)
Here, maximum value of Z + minimum value of Z = 15 - 32 = -17.
View full question & answer→
MCQ 261 Mark
In order for a linear programming problem to have a unique solution, the solution must exist.
  • A
    At the intersection of the nonnegativity constraints.
  • B
    At the intersection of a nonnegativity constraint and a resource constraint.
  • C
    At the intersection of the objective function and a constraint.
  • ✓
    At the intersection of two or more constraints.
Answer
Correct option: D.
At the intersection of two or more constraints.
In order for a linear programming problem to have a unique solution, the solution must exist at the intersection of two or more constraints.
Then the problem becomes convex and has a single optimum (maximum or minimum).
View full question & answer→
MCQ 271 Mark
The feasible region for an LPP is shown shaded in the following figure. Minimum of Z = 4x + 3y occurs at the point.
  • A
    (0, 8)
  • ✓
    (2, 5)
  • C
    (4, 3)
  • D
    (9, 0)
Answer
Correct option: B.
(2, 5)
(2, 5)
View full question & answer→
MCQ 281 Mark
The solution set of the inequation 2x + y > 5 is:
  • A
    half plane that contains the origin
  • ✓
    open half plane not containing the origin
  • C
    whole xy-plane except the points lying on the line 2x + y = 5
  • D
    none of these
Answer
Correct option: B.
open half plane not containing the origin
On putting x = 0, y = 0 in the given inequality, we get 0 > 5, which is absurd.
Therefore, the solution set of the given inequality does not include the origin.
Thus, the solution set of the given inequality consists of the open half plane not containing the origin.
View full question & answer→
MCQ 291 Mark
Which of the following statements about an LP problem and its dual is false?
  • A
    If the primal and the dual both have optimal solutions, the objective function values for both problems are equal at the optimum.
  • B
    If one of the variables in the primal has unrestricted sign, the corresponding constraint in the dual is satisfied with equality.
  • C
    If the primal has an optimal solution, so has the dual.
  • ✓
    The dual problem might have an optimal solution, even though the primal has no (bounded) optimum.
Answer
Correct option: D.
The dual problem might have an optimal solution, even though the primal has no (bounded) optimum.
If one of the problems (primal, dual) is infeasible then the other problem is infeasible.
View full question & answer→
MCQ 301 Mark
Objective of linear programming for an objective function is to:
  • ✓
    Maximize or minimize.
  • B
    Subset or proper set modeling.
  • C
    Row or column modeling.
  • D
    Adjacent modeling.
Answer
Correct option: A.
Maximize or minimize.
In linear programming, the objective function is the linear equation which is representing some quantity (such as profit gained, cost, ...) which is to be maximized or minimized subject to the given constraints.
View full question & answer→
MCQ 311 Mark
In linear programming, objective function and objective constraints are:
  • A
    Solved
  • ✓
    Linear
  • C
    Quadratic
  • D
    Adjacent
Answer
Correct option: B.
Linear
In linear programming, objective function and objective constraints are linear.
Any linear programming problem must have the following properties:-
The relationship between variables and constraints must be linear.
The constraints must be non-negative.
objective function must be linear.
View full question & answer→
MCQ 321 Mark
Minimise $\text{Z}=\sum\limits^{\text{n}}_{\text{j}=1}\sum\limits^{\text{m}}_{\text{i}=1}\text{c}_{\text{ij}}\cdot\text{x}_{\text{ij}}$ Subject to $\sum\limits^{\text{m}}_{\text{i}=1}\text{x}_{\text{ji}}=\text{b}_{\text{j}},\text{j}=1,2,....\text{n}$ $\sum\limits^{\text{n}}_{\text{j}=1}\text{x}_{\text{ji}}=\text{b}_{\text{j}},\text{j}=1,2,.....,\text{m}$ is a $\ce{LPP}$ with number of constraints.
  • A
    $\text{m}-\text{n}$
  • B
    $\text{m}\text{n}$
  • ✓
    $\text{m}+\text{n}$
  • D
    $\frac{\text{m}}{\text{n}}$
Answer
Correct option: C.
$\text{m}+\text{n}$
Constraints will be
$x_{11} ​+ x_{21} ​+ ..... + x_{m1} ​= b_{1​}$
$x_{12}​ + x_{22}​ + ..... + x_{m2}​ = b_{2​}$
$x_{1n}​ + x_{2n} ​+ ..... + xmn​ = b_n​$
$x_{11}​ + x_{12}​ + ..... + x_{1n}​ = b_1​$
$x_{21​}+ x_{22} ​+ ..... + x_{2n} ​= b_{2​}$
$x_{m1} + x_{m2}​ + ..... + x_{mn}​ = b_{n​}$
So the total number of constraints $= m + n$
View full question & answer→
MCQ 331 Mark
The first step in formulating an LP problem is:
  • A
    Graph the problem.
  • B
    Perform a sensitivity analysis.
  • C
    Identify the objective and the constraints.
  • ✓
    Understand the managerial problem being faced.
Answer
Correct option: D.
Understand the managerial problem being faced.
The first step in formulating an linear programming problem is to understand the managerial problem being faced i.e., determine the quantities that are needed to solve the problem.
View full question & answer→
MCQ 341 Mark
Maximize $Z = 10 x_1 + 25 x_2$, subject to $0\leq\text{x}_{1}\leq3,0\leq\text{x}_{2}\leq3,\text{x}_{1}+\text{x}_{2}\leq5.$
  • A
    $80$ at $(3, 2)$
  • B
    $75$ at $(0, 3)$
  • C
    $30$ at $(3, 0)$
  • ✓
    $95$ at $(2, 3)$
Answer
Correct option: D.
$95$ at $(2, 3)$
View full question & answer→
MCQ 351 Mark
The maximum value of Z = 4x + 2y subject to the constraints $2\text{x}+3\text{y}\leq18,\text{x}+\text{y}\geq10,\text{x},\text{y}\leq0$ is:
  • A
    36
  • B
    40
  • C
    30
  • ✓
    None of these
Answer
Correct option: D.
None of these
None of these
View full question & answer→
MCQ 361 Mark
If the constraints in a linear programming problem are changed
  • ✓
    the problem is to be re-evaluated
  • B
    solution is not defined
  • C
    the objective function has to be modified
  • D
    the change in constraints is ignored
Answer
Correct option: A.
the problem is to be re-evaluated
The optimisation of the objective function of a LPP is governed by the constraints.
Therefore, if the constraints in a linear programming problem are changed, then the problem needs to be re-evaluated.
View full question & answer→
MCQ 371 Mark
Objective of LPP is:
  • A
    A constraint
  • ✓
    A function to be optimized
  • C
    A relation between the variables
  • D
    None of the above
Answer
Correct option: B.
A function to be optimized
The objective of Linear Programming Problems (LPP) is to minimize or maximize the function.
View full question & answer→
MCQ 381 Mark
Which of the termis not used in a linear programming problem:
  • A
    Slack inequation
  • B
    Objective function
  • ✓
    Concave region
  • D
    Feasible Region
Answer
Correct option: C.
Concave region
Concave region
View full question & answer→
MCQ 391 Mark
In linear programming, oil companies used to implement resources available is classified as:
  • A
    Implementation modeling
  • ✓
    Transportation models
  • C
    Oil model
  • D
    Resources modeling
Answer
Correct option: B.
Transportation models
In linear programming, transportation model are applied to problems related to the study of efficient transportation routes.
For oil companies, how effectively the available resources are transported to different destinations with minimum cost.
View full question & answer→
MCQ 401 Mark
$Z = 20x_1 + 20x_2$, subject to $\text{x}_1\geq0,\text{x}_{2}\geq0,\text{x}_{1}+2\text{x}_{2}\geq8,3\text{x}_{1}+2\text{x}_{2}\geq15,5\text{x}_{1}+2\text{x}_{2}\geq20.$ The minimum value of $Z$ occurs at
  • A
    $(8, 0)$
  • B
    $\Big(\frac{5}{2},\frac{15}{4}\Big)$
  • ✓
    $\Big(\frac{7}{2},\frac{9}{4}\Big)$
  • D
    $(0, 10)$
Answer
Correct option: C.
$\Big(\frac{7}{2},\frac{9}{4}\Big)$
View full question & answer→
MCQ 411 Mark
The corner points of the feasible region determined by the system of linear constraints are (0, 10),(5, 5),(15, 15),(0, 20). Let z = px + qy where p, q > 0. Condition on p and q so that the maximum of z occurs at both the points (15, 15) and (0, 20) is __________:
  • A
    q = 2p
  • B
    p = 2p
  • C
    p = q
  • ✓
    q = 3p
Answer
Correct option: D.
q = 3p
Let z0​ be the maximum value of z in the feasible region.
Since maximum occurs at both (15, 15) and (0, 20)$, the value z0​ is attained at both (15, 15) and (0, 20).
⟹ z0​ = p(15) + q(15) and z0​ = p(0) + q(20)
⟹ p(15) + q(15) = p(0) + q(20)
⟹ 15p = 5q
⟹ 3p = q
View full question & answer→
MCQ 421 Mark
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 $4\ cm?$
  • A
    $1 : 6$
  • ✓
    $1 : 4$
  • C
    $1 : 2$
  • D
    $3 : 1$
Answer
Correct option: B.
$1 : 4$
Given$: \mathrm{d}_1=2 \mathrm{\sim \ cm}$
$\mathrm{d}_2=4 \mathrm{\sim \ cm}$
Since the diameter are $2 \ cm$ and $4 \ cm .$
The replacement ratio of the two pipes are $1 \ cm$ and $2 \mathrm{ cmr}_1=1 \mathrm{~cm}$
$\mathrm{r}_2=2 \mathrm{\sim \ cm}$
Square of the ratio of the pipes are $1$ and $4$
$\therefore$ The ratio of rates of flow in two pipes $=1: \frac{1}{4}$
$\Rightarrow \frac{1}{4}$
 
View full question & answer→
MCQ 431 Mark
The corner points of the feasible region are A(0, 0), B(16, 0), C(8, 16) and D(0, 24). The minimum value of the objective function z = 300x + 190y is _______.
  • A
    5440
  • B
    4800
  • C
    4560
  • ✓
    0
Answer
Correct option: D.
0
We know that, for a cartesian polygon, the maximum value occurs at the corner points or vertices of the polygon.
Given z = 300x + 190y
By substituting A(0, 0) in the equation we get z = 0
By substituting B(16, 0) in the equation we get z = 4800
By substituting C(8,16) in the equation we get z = 5440
By substituting D(0, 24) in the equation we get z = 4560
Hence the minimum value of Z occured at C(0, 0) with z = 0
View full question & answer→
MCQ 441 Mark
If a = b then ax = ...........
  • A
    b + x
  • ✓
    bx
  • C
    b - x
  • D
    b ÷ x
Answer
Correct option: B.
bx
Given, a = b Multiplying both sides by x.
ax = bx.
View full question & answer→
MCQ 451 Mark
What is the solution of $\text{x}\leq4,\text{y}\geq0$ and $\text{x}\leq-4,\text{y}\geq0$?
  • A
    $\text{x}\geq-4,\text{y}\leq0$
  • B
    $\text{x}\leq4,\text{y}\geq0$
  • ✓
    $\text{x}\leq-4,\text{y}=0$
  • D
    $\text{x}\geq-4,\text{y}=0$
Answer
Correct option: C.
$\text{x}\leq-4,\text{y}=0$
$\text{x}\leq4$ and $\text{x}\leq-4$
$\Rightarrow\text{x}\leq-4$
Also, $\text{y}\geq0$ and $\text{y}\leq0$
$\Rightarrow\text{y}=0$
Hence the solutione is $\text{x}\leq-4,\text{y}=0.$
View full question & answer→
MCQ 461 Mark
The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is:
  • A
    p = q
  • B
    p = 2q
  • C
    q = 2p
  • ✓
    q = 3p
Answer
Correct option: D.
q = 3p
q = 3p
View full question & answer→
MCQ 471 Mark
Which of the following statements is correct?
  • A
    Every $\text{LPP}$ admits an optimal solution
  • B
    A $\text{LPP}$ admits unique optimal solution
  • ✓
    If a $\text{LPP}$ admits two optimal solution it has an infinite number of optimal solutions
  • D
    The set of all feasible solutions of a $\text{LPP}$ is not a converse set
Answer
Correct option: C.
If a $\text{LPP}$ admits two optimal solution it has an infinite number of optimal solutions
Optimal solution of $\text{LPP}$ has three types.
  1. Unique
  2. Infinite
  3. Does not exist.
Hence, it has infinite solution if it admits two optimal solution.
View full question & answer→
MCQ 481 Mark
In order to maximize the profit of the company, the optimal solution of which of the following equations is required?
  • A
    P = x + y - 200
  • ✓
    P = 5y - 2x
  • C
    P = y - 80
  • D
    P = 200 - x
Answer
Correct option: B.
P = 5y - 2x
Let the number of normal calculators produced in a day be x andthe number of scientific calculators produced in a day be y the minimum of total calculators to be produced per day is 200
$\Rightarrow\text{x}+\text{y}\leq200$
Given, the minimum number of normal calculators to be produced per day is 100
$\Rightarrow\text{x}\geq100$
andthe minimum number of scientific calculators to be produced per day is 80
$\Rightarrow\text{y}\geq80$
Also given, the maximum number of normal calculators can be produced per day is 200
$\Rightarrow\text{x}\leq200$
andthe maximum number of scientific calculators can be produced per day is 170
$\Rightarrow\text{x}\leq170$
A normal calculator incurred a loss of Rs. 2
For x normal calculators, the loss is Rs. 2x
A scientific calculator gained a profit of Rs. 5
For xy scientific calculators, the gain is Rs. 5y
Therefore, profit of the manufacturer P = 5y - 2x.
View full question & answer→
MCQ 491 Mark
Choose the correct answer from the given four options.
Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5).
Let F = 4x + 6y be the objective function.
The Minimum value of F occurs at.
  • A
    (0, 2) only.
  • B
    (3, 0) only.
  • C
    The mid point of the line sgment joining the points (0, 2) and (3, 0) only.
  • ✓
    Any point on the line segment joining the points (0, 2) and (3, 0).
Answer
Correct option: D.
Any point on the line segment joining the points (0, 2) and (3, 0).
 
Corner points
Corresponding value of F = 4x + 6y
(0, 2)
12 (Minimum)
(3, 0)
12 (Minimum)
(6, 0)
24
(6, 8)
72 (Maxmimum)
(0, 5)
30
 
View full question & answer→
MCQ 501 Mark
Corner points of the bounded feasible region for an LP problem are A(0, 5) B(0, 3) C(1, 0) D(6, 0). Let z = -50x + 20y be the objective function. Minimum value of z occurs at ______ center point.
  • A
    (0, 5)
  • B
    (1, 0)
  • ✓
    (6, 0)
  • D
    (0, 3)
Answer
Correct option: C.
(6, 0)
We check the value of the z at each of the corner points.
A (0, 5) -z = -50x + 20y = -50(0) + 20(5) = 100
At B (0, 3) -z = -50x + 20y = -50(0) + 20(3) = 60
At C (1, 0) -z = -50x + 20y = -50(1) + 20(0) = -50
At D (6, 0) -z = -50x + 20y = -50(6) + 20(0) = -300
Hence, we see that z is minimum at D(6, 0) and minimum value is -300.
View full question & answer→
Generate Paper FreeAll Linear Programming topics