Solve a nontrivial constrained optimization problem from Raos text using MATLAB only, compare your results with the one provided in the text, extend your studies (if possible) by changing some parameters or adding new ideas, and please show all the results. Wherever necessary, please feel free to choose any appropriate values for the known (but not given) parameters. Also, I would encourage you to use Matlabs Optimtool which is a GUI for solving optimization problems.

Please include problem formulation, solution methodology, and the accurracy of opimization or how to improve.

*If you don't have MATLAB, please use m code syntax when you write out the answer. This will be greatly appreciated.

Example 1.10 A uniform column of rectangular cross section is to be constructed for supporting a water tank of mass M (Fig. 1.14). It is required (1) to minimize the mass verse vibration of the system for avoiding possible resonance due to wind. Formulate the problem of designing the column to avoid failure due to direct compression and buckling. Assume the permissible compressive stress to be max. of the column for economy, and (2) to maximize the natural frequency of trans- Example 1.10 A uniform column of rectangular cross section is to be constructed for supporting a water tank of mass M (Fig. 1.14). It is required (1) to minimize the mass verse vibration of the system for avoiding possible resonance due to wind. Formulate the problem of designing the column to avoid failure due to direct compression and buckling. Assume the permissible compressive stress to be max. of the column for economy, and (2) to maximize the natural frequency of trans