11th Business Maths Monthly Test - 4 (Operations Research )

MABS Institution

11th Business Maths Monthly Test - 4 (Operations Research )-Aug 2020

Time : 2.00 Hours

Part - A

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

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.

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 graphically: Minimize Z = 20x₁ + 40x₂ . Subject to the constraints
\(36{ x }_{ 1 }+6{ x }_{ 2 }\ge 108,\quad 3{ x }_{ 1 }+12{ x }_{ 2 }\ge 36,\quad 20{ x }_{ 1 }+10{ x }_{ 2 }\ge 100\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

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 linear programming problem graphically.
Minimize Z=200x₁+500x₂ subject to the constraints x₁+2x₂≥10; 3x₁+4x₂≤24 and x₁≥0, 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.

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

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

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

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11th Business Maths Monthly Test - 4 (Operations Research )

MABS Institution

11th Business Maths Monthly Test - 4 (Operations Research )-Aug 2020

Part - A

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. Maximize Z= 2 x1 +3x2 subject to constraints x1 + x2 ≤ 30 ; x2 ≤ 12; x1 ≤ 20 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.

Solve graphically: Minimize Z = 20x1 + 40x2 . Subject to the constraints \(36{ x }_{ 1 }+6{ x }_{ 2 }\ge 108,\quad 3{ x }_{ 1 }+12{ x }_{ 2 }\ge 36,\quad 20{ x }_{ 1 }+10{ x }_{ 2 }\ge 100\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

Solve the following linear programming problem graphically. Minimize Z=200x1+500x2 subject to the constraints x1+2x2≥10; 3x1+4x2≤24 and x1≥0, 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.

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

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

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Other Study material

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Tamilnadu Stateboardszs - Class

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.
Maximize Z= 2 x₁ +3x₂ subject to constraints x₁ + x₂ ≤ 30 ; x₂ ≤ 12; x₁ ≤ 20 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.

Solve graphically: Minimize Z = 20x₁ + 40x₂ . Subject to the constraints
\(36{ x }_{ 1 }+6{ x }_{ 2 }\ge 108,\quad 3{ x }_{ 1 }+12{ x }_{ 2 }\ge 36,\quad 20{ x }_{ 1 }+10{ x }_{ 2 }\ge 100\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

Solve the following linear programming problem graphically.
Minimize Z=200x₁+500x₂ subject to the constraints x₁+2x₂≥10; 3x₁+4x₂≤24 and x₁≥0, 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.

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

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