RTU Previous Year Question Papers BE Fourth Optimization in Civil Engineering July 2011

RTU Previous Year Question Papers BE Fourth

Optimization in Civil Engineering July 2011


1. (a) (i) What are the engineering application of optimization methods ? Explain briefly.

(ii) A rectangular plate of size axb is to be used to prepare a box open at top by cutting four rectangular portions at each corners and folding along the edge. Find the size s of the smaller rectangular portions to be cut to obtain the maximum volume in the box.

OR

(b) (i) What are the classifications of optimization problems ? Explain any one in briefly.

(ii) A solid cone is to be moulded by using minimum material and to obtain maximum volume. Find the ratio of base diameter to height.

 

2 (a)What do you mean by a linear programming- problem ? Using Simplex method solve the following linear programming problem ?

(a)  Max z = xj+3 x2 -2xg Subject to

3x1 -x2 +2x3 <=7 -2 Xj +4 x2 <==12 4 X|+3 x2 +8 x3 <-7

Xj, x2, x3 >=0

OR

3 (a)What do you mean by Duality in Linear Programming ? Write the dual of the Linear Programming problem given above in and find the solution.

(b)What do you mean by a sensitivity analysis of linear programming problem ?

Using simplex method solve the following linear programming problem.

Max z = x^+3 x2 -2x3 Subject to

3X} -x2 +2x3 <=7 -2 Xi +4 x2 <=12

4             Xj+3 x2 +8 x3 <=7

xl> x2> x3 >=0

OR

(a) That do you mean by Transportation problem ?

(b) Find and solve the dual of the Linear Programming problem given above.

 

4 (a)What are the methods employed in solving the non­linear optimization problems. Give a brief of any one method.

(b)Find the minimum of the function f = x5 – 5 x3 -20 x + 10 using golden section method, in the interval (0.5)

OR

(a)What do you mean by direct search method employed in solving the Non-linear optimization problems. Give a brief of the method.

(b)Find the minimum of the function f=x^-5x’^ -20 x + 10 using Fibonacci method, in the interval (0,5)

 

5 (a) What do you mean by multi-stage decision in dynamic methods of optimization problems. Give a brief of any one method.

(b) Solve the following LP problem by dynamic programming :

Max z = 5x1 +4 x2 Subject to

OR

(a) What do you mean by dynamic programming in optimization problems. Give a brief of the method.

(b) Differentiate between an initial value problem and final value problem. How to convert an initial value problem and final value problem ?

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