Describe the objective of structural analysis.

(b) Discuss relative merits and demerits of matrix analysis of structures Force methods and displacement methods.
2. Solve the following integer programming using the branch and bound method;
Maximize z =2x1 3x2
Subject to,
6x1 5x2 25
xl 3x2 10
and xl,x2 0 and integers.

3. Analyse the truss shown in Figure 1 for the bar forces. The 10 kN load at the joint is 30° inclined to the vertical. <img src='./qimages/8734-3.jpg'>

4. For the truss of Figure determine the vertical and horizontal displacements of joint B and the horizontal displacement at C.
<img src='./qimages/8734-4.jpg'> Describe the role of sensitivity analysis in Linear Programming.
A company wants to produce three products: B and C. "The per unit profit on these products is RS RS 6 and RS respectively. These products require two types of resources, manpower and raw material. The Linear Programming Model for determining the optimal product mix is as follows:
Maximize z 4x1 6x2 2x3
Subject to,
X1 x2 x3 3 (Manpower required)
X1 4x2 7x3 9 (Raw material available)
and xl, x2, x3 O.
where xl, x2 and x3 number of units of products B and C respectively to be produced. Find the optimal product mix and the corresponding profit of the company.
In the above question, what will be the new optimal mix when per unit profit from product C is increased from RS 2 to RS 10?

6. State and explain the Kuhn-Tucker necessary conditions to achieve relative maximum for Linear Programming Problem.

7. Write short notes on any two of the following:
Static vs Kinematic Matrix in Structural Analysis Duality in Optimization Geometric Programming