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

MABS Institution

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

Time : 1.30 Hours

Part - A

Generic 2 - Answer All Question

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 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.

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.

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

An aeroplane can carry a maximum of 200 passengers. A profit of Rs.1000 is made on each executive class ticket and a profit of Rs. 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximize the profit for the airline. Formulate the mathematical LPP for the above.

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

Draw the logic network for the following:
Activities C and D both follow A, activity E follows C, activity F follows D, activity E and F precedes B.

Part - B

Generic 5 - Answer All Question

Solve the following linear programming problem graphically.
Maximize Z = 3x₁ + 5x₂ subject to the constraints x₁+x₂≤6, x₁≤4; x₂≤5, and x₁, x₂ ≥0

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

Draw 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.

Jobs 1-2 1-3 2-4 3-4 3-5 4-5 4-6 5-6

Duration 6 5 10 3 4 6 2 9
Draw the network diagram for the following activities

Activity code A B C D E F G

Predecessor activity - - A A B C D,E

The following table use the activities in a construction projects and relevant information.

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

Duration (in days) 22 27 12 14 6 12

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.

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

MABS Institution

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

Part - A

Generic 2 - Answer All Question

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 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.

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

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

Draw the logic network for the following: Activities C and D both follow A, activity E follows C, activity F follows D, activity E and F precedes B.

Part - B

Generic 5 - Answer All Question

Solve the following linear programming problem graphically. Maximize Z = 3x1 + 5x2 subject to the constraints x1+x2≤6, x1≤4; x2≤5, and x1, x2 ≥0

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

Draw 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. Jobs 1-2 1-3 2-4 3-4 3-5 4-5 4-6 5-6 Duration 6 5 10 3 4 6 2 9

Draw the network diagram for the following activities Activity code A B C D E F G Predecessor activity - - A A B C D,E

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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 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.

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

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

Draw the logic network for the following:
Activities C and D both follow A, activity E follows C, activity F follows D, activity E and F precedes B.

Solve the following linear programming problem graphically.
Maximize Z = 3x₁ + 5x₂ subject to the constraints x₁+x₂≤6, x₁≤4; x₂≤5, and x₁, x₂ ≥0

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

Draw 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.

Jobs 1-2 1-3 2-4 3-4 3-5 4-5 4-6 5-6

Duration 6 5 10 3 4 6 2 9

Draw the network diagram for the following activities

Activity code A B C D E F G

Predecessor activity - - A A B C D,E