As part of its commitment to sustainability and energy initiatives, Universiti Malaysia Pahang Al-Sultan Abdullah (UMPSA) has successfully implemented a floating solar panel system on the lake within the Pekan campus. This innovative project, launched in 2023, marks UMPSA as the first public university in Malaysia to implement a floating solar system of this scale. The solar system is designed to withstand varying weather conditions and is expected to generate approximately 197,319 kWh of electricity annually, which can offset around 126.1 tonnes of carbon dioxide emissions each year. To evaluate the performance of this solar system, UMPSA engineers conducted a study by recording solar irradiance and the corresponding power output at hourly intervals from 7:30 AM to 3:30 PM on a clear day. Table 1 provides the collected data, showing how solar irradiance (S) and power output (P) vary throughout the day. Table 1: Solar Irradiance and Power Output Measured at Hourly Intervals Power Output Time Solar Irradiance (W/m²) (W) 7:30 AM 50 30 8:30 AM 250 80 9:30 AM 400 100 10:30 AM 600 165.5 11:30 AM 720 215 12:30 PM 800 245.5 1:30 PM 790 235.5 2:30 PM 700 200 3:30 PM 550 150 1) Develop a best fit correlation using the Naïve-Gauss elimination method based on the given data in Table 1 to describe the relationship between power output (P) and solar irradiance (S). Also, calculate the coefficient of determination for the equation. 2) Using Microsoft Excel, plot the power output as a function of solar irradiance based on the data in Table 1. Determine the equation using: i) Linear regression and ii) Polynomial regression. Then, calculate the corresponding coefficient of determination for each regression. Finally, choose the best-fitting correlation and justify your choice. 3) By applying the best-fit correlation obtained from Question (2), estimate the solar irradiance required to produce a power output of 180 W, using a suitable root-finding technique. Continue the iterations until the approximate error falls below 0.1%. 4) The correlation between solar irradiance and time can be expressed by Equation 1. S(t) = -2.5421t³ + 4.2388t² + 190.27t + 48.889 Equation 1 Determine the optimal time at which the solar irradiance reaches its maximum by applying the following methods: a) Golden-section search (&s=1%) b) Newton's method (&s=1%) 5) By referring to the data in Table 1, calculate the power output at 12:00 PM, to the most accurate value. 6) Powering systems using solar energy requires that the panel consistently produces a minimum output of 160 W. To maintain efficient system performance, the solar panel system should be disconnected once the power output drops below this threshold. Recommend the approximate time when the power output falls below 160 W.