What do you understand by a design space in optimization problem?

State the linear programming problem in standard form (either scalar or matrix form).

Develop objective function and design constraints for a minimum-weight design of a prismatic beam as shown in the figure, subject to a limitation on the maximum deflection.

<img src='./qimages/15462-2a.jpg'>

State the limitations of Fibonacci method.

3. A light metal industry manufactures two products A and B. Each product must pass through two processing sections L and M. A good number of machines are available in both sections. Product A requires 2 hours of processing time in Land 1 hour in M. Product B requires 1 hour of processing time in Land 4 hours in M. Total time available in section L is 6,000 hours, whereas in M it is 10,000 hours. The net profit for product A is RS 10 per unit and for B is RS 15 per unit. Formulate this problem as a linear programming model to maximize profit per week.

Describe the distinction between a local minimum and local maximum in unconstrained optimization problem.

The total profit (in rupees) of a beam manufacturing firm (of standard length) from manufacturing and sale of a particular number of beams is given by

y 2x 80,

where y is the total profit (in rupees) and x is the number of beams.

What is the profit per beam when a number of beams are sold to get maximum profit?

Briefly explain the reasons behind the use of partial derivatives while optimizing a multivariable function.

Consider the function,
=x1 2x2 x1x2 x1^2 x2^2.

Determine the maximum or minimum point (if any) of the function.

State the Kuhn-Tucker necessary conditions for constrained multivariable optimization problem.

Find the optimum value of the objective function subject to given constraints mentioned as under:
Maximize z 10x1 x1^2 10x2 x^2
subject to,
x1 x2 14
-x1 x2 6
x1,x2 0

Explain 'Grid Search Method'.

Describe the various steps used in the 'Steepest Descent Method'.

'What do you understand by 'Interpolation Method' in multi-variable optimization technique?

Derive the one-dimensional minimization problem for the following case

Minimize
from the starting point X1 is




along the search direction S is

{1.00
0.25}

Define the following dynamic programming terms:

State variable

Decision variable

Use dynamic programming to solve the following linear programming problem: Maximize 3x1 5x2
subject to,

x1 4
x2 6
3x1 2x2 18
x1,x2 0.

10. Write short notes on any two of the following:

Random Jumping Method

Interior Penalty Function Method

Design Constraints in the Construction of Water Dam