11th Business Maths Monthly Test - 1 ( Operations Research )

MABS Institution

11th Business Maths Monthly Test - 1 ( Operations Research )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

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

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

A solution which maximizes or minimizes the given LPP is called

a solution
a feasible solution
an optimal solution
none of these

The critical path of the following network is

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

The objective of network analysis is to

Minimize total project cost
Minimize total project duration
Minimize production delays, interruption and conflicts
All the above

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

In critical path analysis, the word CPM mean

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

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

Given an L.P.P maximize Z=2x₁+3x₂ subject to the constrains x₁+x₂≤1, 5x₁+5x₂≥0 and x₁≥0, x₂≥0 using graphical method, we observe

No feasible solution
unique optimum solution
multiple optimum solution
none of these

Network problems have advantage in terms of project

Scheduling
Planning
Controlling
All the above

Part - B

Generic 2 - Answer All Question

Construct a network diagram for the following situtation A < B; B < D, E; C <A and 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 fruit grower can use two typ~s of fertilizers in his garden, brand P and brand Q. The amounts (in Kg) of nitrogen, phosphoric acid, potash and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs atIeast 240 kgs of phosphoric acid, at least 270 kg of potash and atmost 310 kg of chlorine. If the grower wants to minimize the amount of nitrogen added to the garden, formulate the above as mathematical LPP.

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

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

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
Develop a network based on the following information:

Activity: A B C D E F G H

Immediate predecessor: - - A B C,D C,D E F

Construct a network diagram for the following situation:
A<D,E; B, D<F; C<G and B<H.

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

Activity A B C D E F

Predecessor activity - - D A B C

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

A producer has 30 and 17 units of labour and capital respectively which he can use to produce two types of goods X and Y. To produce one unit of X, 2 unit of labour and 3 units of capital are required. Similarly, 3 units of labour and 1 unit of capital is required to produce one unit of Y. If X and Yare priced at HOO and H20 per unit respectively, how should the producer use his resources to maximize the total revenue? Formulate the LPP for the above.

Part - C

Generic 3 - Answer All Question

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 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

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

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

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.

Solve the following LPP graphically.
Maximize \(Z=6{ x }_{ 1 }+5{ x }_{ 2 }\) Subject to the constraints \(3{ x }_{ 1 }+5{ x }_{ 2 }\le 15,\quad 5{ x }_{ 1 }+2{ x }_{ 2 }\le 10\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)
Solve the following LPP graphically. Minimize \(Z={ x }_{ 1 }-5{ x }_{ 2 }+20\)
Subject to the constraints \({ x }_{ 1 }-{ x }_{ 2 }\ge 0,\quad { -x }_{ 1 }+2{ x }_{ 2 }\ge 2,\quad { x }_{ 1 }\ge 3,{ x }_{ 2 }\le 4\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

Solve the following LPP graphically. Minimize\(Z=-3{ x }_{ 1 }+4{ x }_{ 2 }\)
Subject to the constraints \({ x }_{ 1 }+2{ x }_{ 2 }\le 8\quad ,{ 3x }_{ 1 }+{ 2x }_{ 2 }\le 12\quad and\quad \quad { x }_{ 1 }\ge 0,{ x }_{ 2 }\ge 2.\)

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

Part - D

Generic 5 - Answer All Question

Solve the following LPP. Maximize Z = 2 x₁ +5x₂ subject to the conditions x₁+ 4x₂ ≤ 24. 3x₁+x₂ ≤ 21, x₁+x₂ ≤ 9 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.

A Project has the following time schedule

Activity 1-2 2-3 2-4 3-5 4-6 5-6

Duration (in days) 6 8 4 9 2 7

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.

A dietician wishes to mix two types of food F₁ and F₂ in such a way that the vitamin contents of the mixture contains atleast 6units of vitamin A and 9 units of vitamin B. Food F₁ costs Rs.50 per kg and F₂ costs Rs 70 per kg. Food F₁ contains 4 units per kg of vitamin A and 6 units per kg of vitamin B while food F₂ contains 5 units per kg of vitamin A and b units per kg of vitamin B. Formulate the above problem as a linear programming problem to minimize the cost of mixture.

The following table gives the characteristics of project

Activity 1-2 1-3 2-3 3-4 3-5 4-6 5-6

Duration (in days) 5 10 3 4 6 6 5

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.

A Project has the following time schedule

Activity 1-2 1-6 2-3 2-4 3-5 4-5 6-7 5-8 7-8

Duration(in days) 7 6 14 5 11 7 11 4 18

Construct the network and calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity and determine the Critical path of the project and duration to complete the project.

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?
Solve the following linear programming problem graphically.
Maximise Z=4x₁+x₂ subject to the constraints x₁+x₂≤50; 3x₁+x₂≤90 and x₁≥0, x₂≥0.

A manufacturer produces two types of steel trunks. He has two machine A and B. For completing, the first type of the trunk requires 3 hours on machine A and 2 hours on machine B, whereas the second type of the trunk requires 3 hours on machine A and 3 hours on machine B. Machines A and B can work at the most for 18 hours and 14 hours per day respectively. He earns a profit of Rs.30 andRs.40 per trunk of the first type and second type respectively. How many trunks of the each type must he make each day to make maximum profit?

Solve the following linear programming problems by graphical method.
(i) Maximize Z = 6x₁ + 8x₂ subject to constraints 30x₁+20x₂≤300; 5x₁+10x₂≤110; and x₁, x₂ > 0.
(ii) Maximize Z =22x₁+ 18x₂ subject to constraints 960x₁+ 640x₂≤15360; x₁≥ x≤20 and x₁, x₂ ≥0.
(iii) Minimize Z= 3x₁+ 2x₁ subject to the constraints 5x₁+ x₂≥10; x₁+x₂≥6; x₁+ 4, x₂ ≥12 and x₁, x₂≥0.
(iv) Maximize Z= 40x₁+ 50x₂ = subject to constraints 30x₁+x₂≤9; x₁+2x₂≤8 and x₁, x₂≥0
(v) Maximize Z= 20x₁+30x₂ subject to constraints 3x₁+3x₂≤36; 5x₁+2x₂≤50; 2x₁+6x₂≤60 and x₁,x₂
(vi) Minimize Z=20x₁+40x₂ subject to the constraints 36x₁+ 6x₂≥108, 3x₁+12x₂≥36, 20x₁+10x₂≥100 and x₁,x₂≥0.

Comment

Add Comment

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

Activity	1-2	1-6	2-3	2-4	3-5	4-5	6-7	5-8	7-8
Duration(in days)	7	6	14	5	11	7	11	4	18

Activity:	A	B	C	D	E	F	G	H
Immediate predecessor:	-	-	A	B	C,D	C,D	E	F

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 - 1 ( Operations Research )

MABS Institution

11th Business Maths Monthly Test - 1 ( Operations Research )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

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

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?

A solution which maximizes or minimizes the given LPP is called

The critical path of the following network is

The objective of network analysis is to

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

In critical path analysis, the word CPM mean

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

Given an L.P.P maximize Z=2x1+3x2 subject to the constrains x1+x2≤1, 5x1+5x2≥0 and x1≥0, x2≥0 using graphical method, we observe

Network problems have advantage in terms of project

Part - B

Generic 2 - Answer All Question

Construct a network diagram for the following situtation A < B; B < D, E; C <A and D < G.

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

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

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

Develop a network based on the following information: Activity: A B C D E F G H Immediate predecessor: - - A B C,D C,D E F

Construct a network diagram for the following situation: A<D,E; B, D<F; C<G and B<H.

Draw a network diagram for the project whose activities and their predecessor relationships are given below Activity A B C D E F Predecessor activity - - D A B C

Part - C

Generic 3 - Answer All Question

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 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

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

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

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

Solve the following LPP graphically. Minimize \(Z={ x }_{ 1 }-5{ x }_{ 2 }+20\) Subject to the constraints \({ x }_{ 1 }-{ x }_{ 2 }\ge 0,\quad { -x }_{ 1 }+2{ x }_{ 2 }\ge 2,\quad { x }_{ 1 }\ge 3,{ x }_{ 2 }\le 4\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

Solve the following LPP graphically. Minimize\(Z=-3{ x }_{ 1 }+4{ x }_{ 2 }\) Subject to the constraints \({ x }_{ 1 }+2{ x }_{ 2 }\le 8\quad ,{ 3x }_{ 1 }+{ 2x }_{ 2 }\le 12\quad and\quad \quad { x }_{ 1 }\ge 0,{ x }_{ 2 }\ge 2.\)

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

Part - D

Generic 5 - Answer All Question

Solve the following LPP. Maximize Z = 2 x1 +5x2 subject to the conditions x1+ 4x2 ≤ 24. 3x1+x2 ≤ 21, x1+x2 ≤ 9 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?

Solve the following linear programming problem graphically. Maximise Z=4x1+x2 subject to the constraints x1+x2≤50; 3x1+x2≤90 and x1≥0, x2≥0.

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?

Given an L.P.P maximize Z=2x₁+3x₂ subject to the constrains x₁+x₂≤1, 5x₁+5x₂≥0 and x₁≥0, x₂≥0 using graphical method, we observe

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

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

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

Develop a network based on the following information:

Activity: A B C D E F G H

Immediate predecessor: - - A B C,D C,D E F

Construct a network diagram for the following situation:
A<D,E; B, D<F; C<G and B<H.

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

Activity A B C D E F

Predecessor activity - - D A B C

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 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

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

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

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

Solve the following LPP graphically. Minimize \(Z={ x }_{ 1 }-5{ x }_{ 2 }+20\)
Subject to the constraints \({ x }_{ 1 }-{ x }_{ 2 }\ge 0,\quad { -x }_{ 1 }+2{ x }_{ 2 }\ge 2,\quad { x }_{ 1 }\ge 3,{ x }_{ 2 }\le 4\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

Solve the following LPP graphically. Minimize\(Z=-3{ x }_{ 1 }+4{ x }_{ 2 }\)
Subject to the constraints \({ x }_{ 1 }+2{ x }_{ 2 }\le 8\quad ,{ 3x }_{ 1 }+{ 2x }_{ 2 }\le 12\quad and\quad \quad { x }_{ 1 }\ge 0,{ x }_{ 2 }\ge 2.\)

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. 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. Maximize Z = 2 x₁ +5x₂ subject to the conditions x₁+ 4x₂ ≤ 24. 3x₁+x₂ ≤ 21, x₁+x₂ ≤ 9 and x₁, x₂ ≥ 0.

Solve the following linear programming problem graphically.
Maximise Z=4x₁+x₂ subject to the constraints x₁+x₂≤50; 3x₁+x₂≤90 and x₁≥0, x₂≥0.