Water is essential for life, and rivers are vital water sources across the world. The Yamuna Action Plan (YAP), one of India's largest river restoration projects, was launched to clean the Yamuna, but its effectiveness (WQI) the Water Quality Index must be measured through cost-benefit, economic and environmental analysis. Therefore, comprehensive pollutant treatment, prevention of further contamination, and community awareness are crucial for sustainable river management.
Implementing the same concept to the river Yamuna, if an initial base line WQI is 35, a quadratic expression is formed to measure the impact of investment of ₹$x$ crore on the WQI i.e., $W(x)$ as $W(x) = 35 + 1.6x - 0.02x^2$, where $x$ is in Rupees in crores Use the given $W(x)$ to answer the following questions:
(i) Find the value of $x$ at the stationary point for the function $W(x)$. [1 mark]
(ii) Find the maximum value of the WQI using the second derivative test? [1 mark]
(iii) (a) If the investment is ₹ 35 crores, find by how much the WQI is short of its maximum achievable value.[2 marks]
Or
(b) Evaluate the WQI when the investment is ₹60 crore. Determine whether this indicates an enhancement or a diminishing return in our objective when compared with the optimum WQI. [2 marks]