11th Business Maths Monthly Test - 2 ( Operations Research )

MABS Institution

11th Business Maths Monthly Test - 2 ( Operations Research )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

The maximum value of the objective function Z = 3x + 5y subject to the constraints x > 0 , y > 0 and 2x + 5y ≤10 is

In the context of network, which of the following is not correct

A network is a graphical representation
A project network cannot have multiple initial and final nodes
An arrow diagram is essentially a closed network
An arrow representing an activity may not have a length and shape

The critical path of the following network is

1 – 2 – 4 – 5
1– 3– 5
1 – 2 – 3 – 5
1 – 2 – 3 – 4 – 5

Which of the following is not correct?

Objective that we aim to maximize or minimize
Constraints that we need to specify
Decision variables that we need to determine
Decision variables are to be unrestricted

In a network while numbering the events which one of the following statement is false?

Event numbers should be unique
Event numbering should be carried out on a sequential basis from left to right
The initial event is numbered 0 or 1
The head of an arrow should always bear a number lesser than the one assigned at the tail of the arrow

In constructing the network which one of the following statement is false?

Each activity is represented by one and only one arrow. (i.e) only one activity can connect any two nodes
Two activities can be identified by the same head and tail events
Nodes are numbered to identify an activity uniquely. Tail node (starting point) should be lower than the head node (end point) of an activity
Arrows should not cross each other

One of the conditions for the activity (i, j) to lie on the critical path is

E_j-E_i=L_j-L_i=t_ij
E_i-E_j=L_j-L_i=t_ij
E_j-E_i=L_i-L_j=t_ij
E_j-E_i=L_j-L_i≠t_ij

A solution which maximizes or minimizes the given LPP is called

a solution
a feasible solution
an optimal solution
none of these

Maximize: z=3x₁+4x₂ subject to 2x₁+x2≤40, 2x₁+5x₂≤180, x₁,x₂≥0 in the LPP, which one of the following is feasible corner point?

x₁=18, x₂=24
x₁=15, x₂=30
x₁=2.5, x₂=35
x₁=20, x₂=19

In critical path analysis, the word CPM mean

Critical path method
Crash project management
Critical project management
Critical path management

Part - B

Generic 2 - Answer All Question

A retired person has Rs. 70,000 to invest and two types of bonds are available in the market for investment. First type of bond yields an annual income of 8% on the amount invested and the second type yields 10% per annum. As per norms, he has to invest a minimum of Rs. 10,000 in the first type and not more than Rs.30,000 in the second type. How should he plan his investment, so as to get maximum returns after one year of investment? Formulate the above as LPP.

Draw the network for the project whose activities with their relationships are given below:
Activities A,D,E can start simultaneously; B,C>A; G,F>D,C; H>E,F.

Construct the network for the projects consisting of various activities and their precedence relationships are as given below:
A, B, C can start simultaneously A <F,E;B<D,C;E,D<G

A toy company manufactures two types of dolls A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is atmost half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of n2 and n6 per doll, how many of each should be produced weekly in order to maximize the profit. Formulate the above as mathematical LPP.

A factory owner purchases two types of machines A and B for his factory. The requirements and the limitations for the machines are as follows:

Machine Area occupied Labour Force Daily Output (in units)

A 1000 m² 12 men 60

B 1200 m² 8 men 40

He has maximum area of 9000 m² available, and 72 skilled labourers who can operate both the machines. How many machines of each type should he buy to maximize the daily output. Formulate the above as LPP.

Machine	Area occupied	Labour Force	Daily Output (in units)
A	1000 m²	12 men	60
B	1200 m²	8 men	40

Construct the network for each the projects consisting of various activities and their precedence relationships are as given below:

Activity A B C D E F G H I J K

Immediate Predecessors - - - A B B C D E H,I F,G

Draw a network diagram for the project whose activities and their predecessor relationships are given below:

Activity: A B C D E F G H I J K

Predecessor activity: - - - A B B C D F H,I F,G

Part - C

Generic 3 - Answer All Question

Construct the network for the projects consisting of various activities and their precedence relationships are as given below:

Immediate Predecessor A B C D E F G H I

Activity B C D,E,F G I H J K L

A soft drink company has two bottling plants C₁ and C₂. Each plant produces three different soft drinks S₁, S₂ and S₃. The production of the two plants in number of bottles per day are:

Product Plant

C₁ C₂

S₁ 3000 1000

S₂ 1000 1000

S₃ 2000 6000

A market survey indicates that during the month of April there will be a demand for 24000 bottles of S₁, 16000 bottles of S₂ and 48000 bottles of S₃. The operating costs, per day, of running plants C₁ and C₂ are respectively Rs.600 and Rs.400. How many days should the firm run each plant in April so that the production cost is minimized while still meeting the market demand? Formulate the above as a linear programming model.

Develop a network based on the following information.

Activity A B C D B E

Immediate Predecessor - - A C E F

Solve the following LPP graphically. \(\\ \therefore \quad Maximize\quad Z=3{ x }_{ 1 }+4{ x }_{ 2 }\)
subject to the constraints \({ x }_{ 1 }+{ x }_{ 2 }\le 4\quad \quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

Construct the network for the following:

Activity A B C D E F

Immediate Predecessor - - - A B C

Activity	A	B	C	D	E	F
Immediate Predecessor	-	-	-	A	B	C

Solve the following LPP graphically. Maximize \(Z={ x }_{ 1 }+{ x }_{ 2 }\)
Subject to the constraints \({ x }_{ 1 }-{ x }_{ 2 }\le -1,{ -x }_{ 1 }+{ x }_{ 2 }\le 0\quad and\quad { x }_{ 1 }+{ x }_{ 2 }\ge 0\)

Solve the following LPP graphically.
Maximize \(Z=6{ x }_{ 1 }+5{ x }_{ 2 }\) Subject to the constraints \(3{ x }_{ 1 }+5{ x }_{ 2 }\le 15,\quad 5{ x }_{ 1 }+2{ x }_{ 2 }\le 10\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

Part - D

Generic 5 - Answer All Question

Minimize and maximize Z =x₁+ 2x₂ . Subject to the constraints \({ x }_{ 1 }+2{ x }_{ 2 }\ge 100,\quad { 2x }_{ 1 }-{ x }_{ 2 }\le 0,{ \quad 2x }_{ 1 }+{ x }_{ 2 }\le 200\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 10\)

A company manufactures two models of voltage stabilizers viz., ordinary and autocut. All components of the stabilizers are purchased from outside sources, assembly and testing is carried out at company’s own works. The assembly and testing time required for the two models are 0.8 hour each for ordinary and 1.20 hours each for auto-cut. Manufacturing capacity 720 hours at present is available per week. The market for the two models has been surveyed which suggests maximum weekly sale of 600 units of ordinary and 400 units of auto-cut. Profit per unit for ordinary and auto-cut models has been estimated at Rs 100 and Rs 150 respectively. Formulate the linear programming problem.

Solve the following LPP by graphical method Minimize z = 5x1+4x2 Subject to constraints 4x₁+ x₂ ≥ 40 ; 2x₁+3x₂ ≥ 90 and x₁, x₂ > 0.

The following table use the activities in a building project.

Activity 1-2 1-3 2-3 2-4 3-4 4-5

Duration (days) 21 26 11 13 5 11

Draw the network for the project, calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity and find the critical path. Compute the project duration.

Activity	1-2	1-3	2-3	2-4	3-4	4-5
Duration (days)	21	26	11	13	5	11

Solve the following LPP.
Maximize Z= 2 x₁ +3x₂ subject to constraints x₁ + x₂ ≤ 30 ; x₂ ≤ 12; x₁ ≤ 20 and x₁, x₂≥ 0.
Every gram of wheat provides 0.1 g of proteins and 0.25 g of carbohydrates. The corresponding values of rice are 0.05 g and 0.5 g respectively. Wheat cost Rs.4 per kg and rice cost Rs.6 per kg. The minimum daily requirements of proteins and carbohydrate for an average child are 50 g and 200 g respectively. In what quantities should wheat and rice be mixed in the daily diet to provide minimum daily requirements of proteins and carbohydrate at minimum cost. Frame an LPP and solve it graphically.

One kind of the cake requires 200 g of flour and 25 g of fat, and another kind of cake requires 100 g of flour and 50 g of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of other ingredients used in making the cakes?

Comment

Add Comment

Product	Plant
Product	C₁	C₂
S₁	3000	1000
S₂	1000	1000
S₃	2000	6000

InstaQB

Institutions

12th Standard English Medium

12th Standard Tamil Medium

11th Standard English Medium

11th Standard Tamil Medium

10th Standard English Medium

9th Standard English Medium

8th Standard English Medium

7th Standard English Medium

Class XII

Class XI

12Th Standard

11Th Standard

10Th Standard

9Th Standard

11th Business Maths Monthly Test - 2 ( Operations Research )

MABS Institution

11th Business Maths Monthly Test - 2 ( Operations Research )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

The maximum value of the objective function Z = 3x + 5y subject to the constraints x > 0 , y > 0 and 2x + 5y ≤10 is

In the context of network, which of the following is not correct

The critical path of the following network is

Which of the following is not correct?

In a network while numbering the events which one of the following statement is false?

In constructing the network which one of the following statement is false?

One of the conditions for the activity (i, j) to lie on the critical path is

A solution which maximizes or minimizes the given LPP is called

Maximize: z=3x1+4x2 subject to 2x1+x2≤40, 2x1+5x2≤180, x1,x2≥0 in the LPP, which one of the following is feasible corner point?

In critical path analysis, the word CPM mean

Part - B

Generic 2 - Answer All Question

Draw the network for the project whose activities with their relationships are given below: Activities A,D,E can start simultaneously; B,C>A; G,F>D,C; H>E,F.

Construct the network for the projects consisting of various activities and their precedence relationships are as given below: A, B, C can start simultaneously A <F,E;B<D,C;E,D<G

Construct the network for each the projects consisting of various activities and their precedence relationships are as given below: Activity A B C D E F G H I J K Immediate Predecessors - - - A B B C D E H,I F,G

Draw a network diagram for the project whose activities and their predecessor relationships are given below: Activity: A B C D E F G H I J K Predecessor activity: - - - A B B C D F H,I F,G

Part - C

Generic 3 - Answer All Question

Construct the network for the projects consisting of various activities and their precedence relationships are as given below: Immediate Predecessor A B C D E F G H I Activity B C D,E,F G I H J K L

Develop a network based on the following information. Activity A B C D B E Immediate Predecessor - - A C E F

Solve the following LPP graphically. \(\\ \therefore \quad Maximize\quad Z=3{ x }_{ 1 }+4{ x }_{ 2 }\) subject to the constraints \({ x }_{ 1 }+{ x }_{ 2 }\le 4\quad \quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

Construct the network for the following: Activity A B C D E F Immediate Predecessor - - - A B C

Solve the following LPP graphically. Maximize \(Z={ x }_{ 1 }+{ x }_{ 2 }\) Subject to the constraints \({ x }_{ 1 }-{ x }_{ 2 }\le -1,{ -x }_{ 1 }+{ x }_{ 2 }\le 0\quad and\quad { x }_{ 1 }+{ x }_{ 2 }\ge 0\)

Solve the following LPP graphically. Maximize \(Z=6{ x }_{ 1 }+5{ x }_{ 2 }\) Subject to the constraints \(3{ x }_{ 1 }+5{ x }_{ 2 }\le 15,\quad 5{ x }_{ 1 }+2{ x }_{ 2 }\le 10\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

Part - D

Generic 5 - Answer All Question

Minimize and maximize Z =x1+ 2x2 . Subject to the constraints \({ x }_{ 1 }+2{ x }_{ 2 }\ge 100,\quad { 2x }_{ 1 }-{ x }_{ 2 }\le 0,{ \quad 2x }_{ 1 }+{ x }_{ 2 }\le 200\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 10\)

Solve the following LPP by graphical method Minimize z = 5x1+4x2 Subject to constraints 4x1+ x2 ≥ 40 ; 2x1+3x2 ≥ 90 and x1, x2 > 0.

Solve the following LPP. Maximize Z= 2 x1 +3x2 subject to constraints x1 + x2 ≤ 30 ; x2 ≤ 12; x1 ≤ 20 and x1, x2≥ 0.

One kind of the cake requires 200 g of flour and 25 g of fat, and another kind of cake requires 100 g of flour and 50 g of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of other ingredients used in making the cakes?

Comment

Other Study material

11th Business Maths Monthly Test - 3 ( Differentia

11th Business Maths Monthly Test - 4 (Operations R

11th Business Maths Weekly Test - 2 ( Applications

11th Business Maths Weekly Test - 1 ( Applications

11th Business Maths Monthly Test - 4 ( Differentia

11th Business Maths Weekly Test - 4 ( Differential

11th Business Maths Weekly Test - 3 ( Differentia

11th Business Maths Weekly Test -2 ( Differential

11th Business Maths Weekly Test - 1 ( Differential

11th Business Maths Monthly Test - 4 ( Trigonometr

11th Business Maths Monthly Test - 3 ( Trigonometr

11th Business Maths Monthly Test - 2 ( Trigonometr

11th Business Maths Monthly Test - 1 ( Trigonometr

11th Business Maths Weekly Test - 4 ( Trigonometry

11th Business Maths Monthly Test - 1 ( Differentia

Tamilnadu Stateboardszs - Class

Maximize: z=3x₁+4x₂ subject to 2x₁+x2≤40, 2x₁+5x₂≤180, x₁,x₂≥0 in the LPP, which one of the following is feasible corner point?

Draw the network for the project whose activities with their relationships are given below:
Activities A,D,E can start simultaneously; B,C>A; G,F>D,C; H>E,F.

Construct the network for the projects consisting of various activities and their precedence relationships are as given below:
A, B, C can start simultaneously A <F,E;B<D,C;E,D<G

Construct the network for each the projects consisting of various activities and their precedence relationships are as given below:

Activity A B C D E F G H I J K

Immediate Predecessors - - - A B B C D E H,I F,G

Draw a network diagram for the project whose activities and their predecessor relationships are given below:

Activity: A B C D E F G H I J K

Predecessor activity: - - - A B B C D F H,I F,G

Construct the network for the projects consisting of various activities and their precedence relationships are as given below:

Immediate Predecessor A B C D E F G H I

Activity B C D,E,F G I H J K L

Develop a network based on the following information.

Activity A B C D B E

Immediate Predecessor - - A C E F

Solve the following LPP graphically. \(\\ \therefore \quad Maximize\quad Z=3{ x }_{ 1 }+4{ x }_{ 2 }\)
subject to the constraints \({ x }_{ 1 }+{ x }_{ 2 }\le 4\quad \quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

Construct the network for the following:

Activity A B C D E F

Immediate Predecessor - - - A B C

Solve the following LPP graphically. Maximize \(Z={ x }_{ 1 }+{ x }_{ 2 }\)
Subject to the constraints \({ x }_{ 1 }-{ x }_{ 2 }\le -1,{ -x }_{ 1 }+{ x }_{ 2 }\le 0\quad and\quad { x }_{ 1 }+{ x }_{ 2 }\ge 0\)

Solve the following LPP graphically.
Maximize \(Z=6{ x }_{ 1 }+5{ x }_{ 2 }\) Subject to the constraints \(3{ x }_{ 1 }+5{ x }_{ 2 }\le 15,\quad 5{ x }_{ 1 }+2{ x }_{ 2 }\le 10\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

Minimize and maximize Z =x₁+ 2x₂ . Subject to the constraints \({ x }_{ 1 }+2{ x }_{ 2 }\ge 100,\quad { 2x }_{ 1 }-{ x }_{ 2 }\le 0,{ \quad 2x }_{ 1 }+{ x }_{ 2 }\le 200\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 10\)

Solve the following LPP by graphical method Minimize z = 5x1+4x2 Subject to constraints 4x₁+ x₂ ≥ 40 ; 2x₁+3x₂ ≥ 90 and x₁, x₂ > 0.

Solve the following LPP.
Maximize Z= 2 x₁ +3x₂ subject to constraints x₁ + x₂ ≤ 30 ; x₂ ≤ 12; x₁ ≤ 20 and x₁, x₂≥ 0.