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MML Unit 05, 04 QB

The document contains a question bank for linear programming problems and numerical integration techniques. It includes problems to be solved graphically and using the simplex method for linear programming, as well as various numerical integration methods like the Trapezoidal rule and Simpson's rule. Each problem specifies the objective function and constraints for the linear programming tasks, and the intervals and functions for the integration tasks.

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Uzair Borkar
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16 views3 pages

MML Unit 05, 04 QB

The document contains a question bank for linear programming problems and numerical integration techniques. It includes problems to be solved graphically and using the simplex method for linear programming, as well as various numerical integration methods like the Trapezoidal rule and Simpson's rule. Each problem specifies the objective function and constraints for the linear programming tasks, and the intervals and functions for the integration tasks.

Uploaded by

Uzair Borkar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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QUESTION BANK

UNIT 05 (LPP)
1) Solve the following linear programming problem graphically to find solution.
Maximize, Z = 2x + 5y
Subject to, x + 2y ≤ 16
5x + 3y ≤ 45
x ≥ 0, y ≥ 0
2) Solve the following linear programming problem using simplex method to find
solution.
Maximize, Z = 12x1 + 16x2
Subject to, 10x1 + 20x2 ≤ 120
8x1 + 8x2 ≤ 80
x1 ≥ 0, x2 ≥ 0
3) Solve the following linear programming problem using simplex method to find
solution.
Maximize, Z = 3x + 2y
Subject to, x+y≤4
x-y≤2
x ≥ 0, y ≥ 0
4) Solve the following linear programming problem using simplex method to find
solution.
Maximize, Z = 3x1 + 4x2
Subject to, x1 + x2 ≤ 450
2x1 + x2 ≤ 600
x1 ≥ 0, x2 ≥ 0
5) Solve the following linear programming problem graphically to find solution.
Maximize, Z = 11x + 8y
Subject to, x ≤4
y≤6
x+y≤6
x ≥ 0, y ≥ 0
6) Solve the following linear programming problem graphically to find solution.
Maximize, Z = x1 + 2x2
Subject to, x1 + 2x2 ≤ 20
x1 + x2 ≤ 12
x ≥ 0, y ≥ 0

QUESTION BANK
UNIT 04
71
1) Evaluate: ∫2 𝑑𝑥 , using Trapezoidal rule and by dividing interval [2 ,7] into five
𝑥
equal sub intervals.
5 1
2) Compute ∫1 𝑑𝑥, using Simpson’s one third rule and by dividing interval [1 ,5]
𝑥+2
into four equal sub intervals.
6
3) Using Trapezoidal rule evaluate:- ∫0 𝑓(𝑥) 𝑑𝑥 given by
x 0 1 2 3 4 5 6

f(x) 1 0.5 0.3333 0.25 0.2 0.6666 0.1428


21
4) Using Simpson’s one third rule evaluate:- ∫1 𝑑𝑥 given by
𝑥
x 1 1.25 1.5 1.75 2

f(x) 1 0.8 0.666 0.5714 0.5


6 1
5) Compute ∫0 𝑑𝑥, using Simpson’s 3/8 rule
1+𝑥 2
2
6) Evaluate: ∫0 (1 + 𝑥 3 ) 𝑑𝑥, using Trapezoidal rule and by dividing interval [0 ,2]
into four equal sub intervals.
2
7) Using Simpson’s one third rule evaluate:- ∫0 𝑒 −𝑥 𝑑𝑥 given by
x 0 1/2 1 3/2 2

f(x) 1 0.6064 0.3676 0.2331 001353


𝜋
𝜋
8) Evaluate: ∫02 𝑐𝑜𝑠𝑥 𝑑𝑥 , using Trapezoidal rule and by dividing interval [0 , 2 ] into
three equal sub intervals.
𝜋
9) Compute ∫0 √𝑐𝑜𝑠𝑥 𝑑𝑥, using Simpson’s 3/8 rule with n = 8
2

10) Write the Simpson’s one third and Simpson’s 3/8 rule formula for numerical
integration.

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