Linear Programming · Mathematics · MHT CET

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MCQ (Single Correct Answer)

1

The correct constraints for the given feasible region are ….

MHT CET 2025 22nd April Evening Shift
2

If the difference between the maximum and minimum values of the objective function $\mathrm{z}=7 x-8 y$, subject to the constraints $x+y \leqslant 20, y \geqslant 5, x, y \geqslant 0$ is $5 \mathrm{k}+200$, then the value of k is

MHT CET 2025 22nd April Morning Shift
3

The solution set for minimizing the function $\mathrm{z}=x+y$ with constraints $x+y \geqslant 2, x+2 y \leqslant 8, y \leqslant 3, x, y \geqslant 0$ contains

MHT CET 2025 21st April Evening Shift
4

The L.P.P. , minimize $z=30 x+20 y, x+y \leq 8$, $x+2 y \geq 4,6 x+4 y \geq 12, x \geqslant 0, y \geqslant 0$ has

MHT CET 2025 21st April Morning Shift
5

A scholarship amount is given by $\mathrm{z}=550 x+300 y$ and is to be distributed among $x$ boys and $y$ girls. From the graph given below the maximum amount of scholarship is __________

MHT CET 2025 20th April Evening Shift Mathematics - Linear Programming Question 4 English
MHT CET 2025 20th April Evening Shift
6

The shaded region in the following figure represents a solution set of

MHT CET 2025 20th April Morning Shift Mathematics - Linear Programming Question 6 English
MHT CET 2025 20th April Morning Shift
7

The feasible region for the constraints $x-2 \leqslant y, x \geqslant y-1, x \geqslant 2, y \leqslant 4, x, y \geqslant 0$, is _________

MHT CET 2025 19th April Evening Shift
8

The feasible region represented by the given constraints $2 x+3 y \geq 12,-x+y \leq 3, x \leq 4, y \geq 3$ is denoted by

MHT CET 2025 19th April Morning Shift Mathematics - Linear Programming Question 5 English

MHT CET 2025 19th April Morning Shift
9

The shaded area in the given figure is a solution set for some system of inequalities. The maximum value of the function $\mathrm{z}=4 x+3 y$ subject to linear constraints given by the system is

MHT CET 2024 16th May Evening Shift Mathematics - Linear Programming Question 8 English

MHT CET 2024 16th May Evening Shift
10

Maximum value of $Z=100 x+70 y$ Subject to $2 x \geq 4, y \leq 3, x+y \leq 8, x, y \geq 0$ is

MHT CET 2024 16th May Morning Shift
11

The graphical solution set of the system of inequations $2 x+3 y \leq 6, x+4 y \geq 4, x \geq 0, y \geq 0$ is given by

MHT CET 2024 15th May Evening Shift Mathematics - Linear Programming Question 10 English

MHT CET 2024 15th May Evening Shift
12

The region represented by the inequations $2 x+3 y \leqslant 18, x+y \geqslant 10, x \geqslant 0, y \geqslant 0$ is

MHT CET 2024 15th May Morning Shift
13

A production unit makes special type of metal chips by combining copper and brass. The standard weight of the chip must be at least 5 gms. The basic ingredients i.e. copper and brass cost ₹8 and ₹ 5 per gm. The durability considerations dictate that the metal chip must no contain more than 4 gms of brass and should contain minimum 2 gms of copper. Then the minimum cost of the metal chip satisfying the above conditions is

MHT CET 2024 11th May Evening Shift
14

For the following shaded region, the linear constraints are

MHT CET 2024 11th May Morning Shift Mathematics - Linear Programming Question 13 English

MHT CET 2024 11th May Morning Shift
15

The graphical solution set of the system of inequations $x+y \geq 1,7 x+9 y \leq 63, y \leq 5, x \leq 6$, $x \geq 0, y \geq 0$ is represented by

MHT CET 2024 10th May Evening Shift Mathematics - Linear Programming Question 15 English

MHT CET 2024 10th May Evening Shift
16

The function to be maximized is given by $Z=3 x+2 y$. The feasible region for this function is the shaded region given below, then the linear constraints for this region are given by

MHT CET 2024 10th May Morning Shift Mathematics - Linear Programming Question 14 English

MHT CET 2024 10th May Morning Shift
17

The maximum value of $z=4 x+2 y$, subject to the constraints $3 x+4 y \geqslant 12, x+y \leqslant 5, x, y \geqslant 0$ is

MHT CET 2024 9th May Evening Shift
18

The maximum value of $z=x+y$, subjected to $x+y \leq 10,5 x+3 y \geq 15, x \leq 6, x, y \geq 0$

MHT CET 2024 9th May Morning Shift
19

The maximum value of the objective function $\mathrm{z}=4 x+6 y$ subject to $3 x+2 y \leq 12, x+y \geq 4, x$, $y \geq 0$ is

MHT CET 2024 4th May Evening Shift
20

The shaded region in the following figure is the solution set of the inequations

MHT CET 2024 4th May Morning Shift Mathematics - Linear Programming Question 19 English

MHT CET 2024 4th May Morning Shift
21

The maximum value of $\mathrm{Z}=x+y$, subjected to $x+y \leq 10,5 x+3 y \geq 15, x \leq 6, x, y \geq 0$

MHT CET 2024 3rd May Evening Shift
22

The shaded area in the figure below is the solution set for a certain linear programming problem, then the linear constraints are given by

MHT CET 2024 3rd May Morning Shift Mathematics - Linear Programming Question 21 English

MHT CET 2024 3rd May Morning Shift
23

The shaded region in the following figure is the solution set of the inequations

MHT CET 2024 2nd May Evening Shift Mathematics - Linear Programming Question 22 English

MHT CET 2024 2nd May Evening Shift
24

The point, at which the maximum value of $10 x+6 y$ subject to the constraints $x+y \leq 12$, $2 x+y \leq 20, x \geq 0, y \geq 0$ occurs, is

MHT CET 2024 2nd May Morning Shift
25

The shaded region in the following figure represents the solution set for a certain linear programming problem. Then linear constraints for this region are given by

MHT CET 2023 14th May Evening Shift Mathematics - Linear Programming Question 39 English

MHT CET 2023 14th May Evening Shift
26

The solution set of the inequalities $$4 x+3 y \leq 60, y \geq 2 x, x \geq 3, x, y \geq 0$$ is represented by region

MHT CET 2023 14th May Morning Shift Mathematics - Linear Programming Question 41 English

MHT CET 2023 14th May Morning Shift
27

The shaded area in the given figure is a solution set for some system of inequations. The maximum value of the function $$z=10 x+25 y$$ subject to the linear constraints given by the system is

MHT CET 2023 13th May Evening Shift Mathematics - Linear Programming Question 40 English

MHT CET 2023 13th May Evening Shift
28

If feasible region is as shown in the figure, then related inequalities are

MHT CET 2023 13th May Morning Shift Mathematics - Linear Programming Question 42 English
MHT CET 2023 13th May Morning Shift
29

The maximum value of $$z=7 x+8 y$$ subject to the constraints $$x+y \leq 20, y \geq 5, x \leq 10, x \geq 0, y \geq 0$$ is

MHT CET 2023 12th May Evening Shift
30

For a feasible region OCDBO given below, the maximum value of the objective function $$z=3 x+4 y$$ is

MHT CET 2023 12th May Morning Shift Mathematics - Linear Programming Question 43 English

MHT CET 2023 12th May Morning Shift
31

The maximum value of $$z=3 x+5 y$$ subject to the constraints $$3 x+2 y \leq 18, x \leq 4, y \leq 6, x, y \geq 0$$, is

MHT CET 2023 11th May Evening Shift
32

For the following shaded area, the linear constraints except $$x,y \ge 0$$ are

MHT CET 2023 11th May Morning Shift Mathematics - Linear Programming Question 47 English

MHT CET 2023 11th May Morning Shift
33

The shaded area in the figure given below is a solution set of a system of inequations. The minimum value of objective function $$3 x+5 y$$, subject to the linear constraints given by this system of inequations is

MHT CET 2023 10th May Evening Shift Mathematics - Linear Programming Question 48 English

MHT CET 2023 10th May Evening Shift
34

The vertices of the feasible region for the constraints $$x+y \leq 4, x \leq 2, y \leq 1, x+y \geq 1, x, y \geq 0$$ are

MHT CET 2023 10th May Morning Shift
35

The graphical solution set for the system of inequations $$x-2 y \leq 2,5 x+2 y \geq 10,4 x+5 y \leq 20, x \geq 0, y \geq 0$$ is given by

MHT CET 2023 9th May Evening Shift Mathematics - Linear Programming Question 49 English

MHT CET 2023 9th May Evening Shift
36

If feasible region is as shown in the figure, then the related inequalities are

MHT CET 2023 9th May Morning Shift Mathematics - Linear Programming Question 50 English

MHT CET 2023 9th May Morning Shift
37

Maximum value of $$Z=5 x+2 y$$, subject to $$2 x-y \geq 2, x+2 y \leq 8$$ and $$x, y \geq 0$$ is

MHT CET 2022 11th August Evening Shift
38

The region represented by the inequalities $$x \geq 6, y \geq 3,2 x+y \geq 10, x \geq 0, y \geq 0$$ is

MHT CET 2021 24th September Evening Shift
39

The common region of the solutions of the inequations $$x+2 y \geq 4,2 x-y \leq 6$$ and $$x, y>0$$ is

MHT CET 2021 24th September Morning Shift
40

The minimum value of the objective function $$z=4 x+6 y$$ subject to $$x+2 y \geq 80,3 x+y \geq 75, x, y \geq 0$$ is

MHT CET 2021 23rd September Evening Shift
41

The maximum value of the objective function $$z=2 x+3 y$$ subject to the constraints $$x+y \leq 5,2 x+y \geq 4$$ and $$x \geq 0, y \geq 0$$ is

MHT CET 2021 23th September Morning Shift
42

The common region of the solution of the inequations $$x+y \geq 5, y \leq 4, x \geq 2, x, y \geq 0$$ is

MHT CET 2021 22th September Evening Shift
43

The maximum value of $$z=10 x+25 y$$ subject to $$0 \leq x \leq 3,0 \leq y \leq 3, x+y \leq 5$$ occurs at the point.

MHT CET 2021 22th September Morning Shift
44

The objective function $$z=4 x+5 y$$ subjective to $$2 x+y \geq 7 ; 2 x+3 y \leq 15 ; y \leq 3, x \geq 0 ; y \geq 0$$ has minimum value at the point.

MHT CET 2021 21th September Evening Shift
45

The shaded figure given below is the solution set for the linear inequations. Choose the correct option.

MHT CET 2021 21th September Morning Shift Mathematics - Linear Programming Question 53 English

MHT CET 2021 21th September Morning Shift
46

The solution set for the system of linear inequations $$x+y \geq 1 ; 7 x+9 y \leq 63 ; y \leq 5 ; x \leq 6, x \geq 0$$ and $$y \geq 0$$ is represented graphically in the figure. What is the correct option?

MHT CET 2021 20th September Evening Shift
47

The shaded part of the given figure indicates the feasible region. Then the constraints are

MHT CET 2021 20th September Morning Shift Mathematics - Linear Programming Question 55 English

MHT CET 2021 20th September Morning Shift
48

The LPP to maximize $Z=x+y$, subject to $x+y \leq 1,2 x+2 y \geq 6, x \geq 0, y \geq 0$ has

MHT CET 2020 19th October Evening Shift
49

The maximum value of $$Z=3 x+5 y$$, subject to $$3 x+2 y \leq 18, x \leq 4, y \leq 6, x, y \geq 0$$ is

MHT CET 2020 16th October Evening Shift
50

The minimum value of $$Z=5 x+8 y$$ subject to $$x+y \geq 5,0 \leq x \leq 4, y \geq 2, x \geq 0, y \geq 0$$ is

MHT CET 2020 16th October Morning Shift
51

If $z=a x+b y ; a, b>0$ subject to $x \leq 2, y \leq 2, x+y \geq 3, x \geq 0, y \geq 0$ has minimum value at $(2,1)$ only, then......

MHT CET 2019 3rd May Morning Shift
52

The maximum value of $Z=5 x+4 y$, Subject to $y \leq 2 x, x \leq 2 y, x+y \leq 3, x \geq 0, y \geq 0$ is ........

MHT CET 2019 3rd May Morning Shift
53

The maximum value of $z=6 x+8 y$ subject to $x-y \geq 0, x+3 y \leq 12, x \geq 0, y \geq 0$ is $\ldots \ldots$.

MHT CET 2019 2nd May Evening Shift
54

For L.P.P, maximize $z=4 x_1+2 x_2$ subject to $3 x_1+2 x_2 \geq 9, x_1-x_2 \leq 3, x_1 \geq 0, x_2 \geq 0$ has

MHT CET 2019 2nd May Evening Shift
55

The maximum value of $z=9 x+11 y$ subject to $3 x+2 y \leq 12,2 x+3 y \leq 12, x \geq 0, y \geq 0$ is $\ldots \ldots$.

MHT CET 2019 2nd May Morning Shift
56

The minimum value of $z=10 x+25 y$ subject to $0 \leq x \leq 3,0 \leq y \leq 3, x+y \geq 5$ is $\ldots$

MHT CET 2019 2nd May Morning Shift
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