QUESTION 4. Optimization via Golden Section Search by Hand and using MATLAB. [Show the hand calculations for Part 1. Include the M file and the iterative results for Part II] {Mark: 7;3.5, 3.5)

The performance of a system, y = In x sin[x/(5y)]/x, where x/(5y) is in radians, and y is unimodal between 1 GE x LE 11. Optimize the performance using the Golden Section Search.

y = 8

Part I. Show the first 3 iterations step-by-step by hand.

Part II Use MATLAB to optimize the performance until the approximate relative error is less than 5%.