Principle: Development of Each and Every Person to His or Her Greatest Efficiency and Prosperity. Taylor believed in scientifically selecting and assigning tasks suited to each individual's physical, mental, and intellectual capabilities.
Techniques:
1. Method Study: Finding the one best way to perform a task, minimizing production costs while maximizing quality and customer satisfaction.
2. Standardisation: Setting benchmarks for business activities to ensure uniformity and consistency in production.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).