We would like to carry a metal piece of length L (ignore the thickness) in horizontal position around a corner from a corridor of 2 meters wide into a corridor of 3 meters wide as shown in the figure below. In the figure, the metal piece is shown with black color. What is the maximum length that the metal piece can have? a) Write down the function that needs to be optimized. b) Optimize the function you have written in (a) using one of the numerical methods you have learned. Explain your solution in detail including initialization and stopping criterion. You may use a table to show your parameters at each iteration. Note 1: If you wish, you may use Matlab/Octave if it is necessary for your method of choice. If you do so, you must also submit your code. Note 2: If you wish, you can also solve the problem analytically and compare with your numerical solution. 2m 3m corridor