Comparison of Internet Plans - Compare two different internet plans, and determine which plan offers best value. Interpretation and Reflection Data Interpretation - Analyse your collected data and write two key insights about students' online learning experiences Challenges and Solutions - Identify one major challenge students face in online learning and suggest a mathematical solution to address this challenge. Personal Reflection - Write a short paragraph reflecting on how online learning affects students' study habits and finances. Use findings from your investigation to support your answer.

### 1. Comparison of Internet Plans Assume we have two internet plans: - **Plan A:** \(50\) Mbps for \(\$40\) per month. - **Plan B:** \(100\) Mbps for \(\$55\) per month. We calculate the cost per Mbps for each plan: - For Plan A: \[ \text{Cost per Mbps} = \frac{40}{50} = 0.8 \quad \text{dollars per Mbps} \] - For Plan B: \[ \text{Cost per Mbps} = \frac{55}{100} = 0.55 \quad \text{dollars per Mbps} \] Since \(0.55 < 0.8\), **Plan B** offers the best value. --- ### 2. Data Interpretation From the analysis of collected data about students' online learning experiences, two key insights are: - **Insight 1:** Many students report that the convenience of attending classes from home leads to increased flexibility in managing their time; however, it sometimes reduces the opportunities for interactive, face-to-face discussions. - **Insight 2:** Students experience challenges in balancing screen time with mental fatigue, indicating that prolonged online sessions can lead to difficulty in maintaining concentration and overall engagement. --- ### 3. Challenges and Solutions One major challenge in online learning is **network congestion during peak usage times**, which leads to lag, interruptions, and decreased learning efficiency. A mathematical solution to address this challenge is to implement a **linear programming model** to optimize bandwidth allocation. Suppose we define: - \( x_i \) as the fraction of the total available bandwidth allocated to student \( i \), - \( B \) as the total available bandwidth, - \( L(x_i) \) as the latency experienced by student \( i \). We can then set up the optimization problem as follows: \[ \text{Minimize} \quad L = \sum_{i=1}^{n} L(x_i) \] subject to: \[ \sum_{i=1}^{n} x_i \leq B \] \[ x_i \geq 0 \quad \text{for all } i. \] This model would help in determining the optimal allocation of bandwidth to minimize overall latency during peak times. --- ### 4. Personal Reflection Online learning has significantly reshaped students' study habits and financial planning. With the flexibility of attending classes from any location, students have adopted more self-directed study routines, often balancing coursework with part-time jobs or other commitments. However, the reduction in on-campus interactions can affect motivation, leading some students to struggle with procrastination and reduced engagement. Additionally, while some costs related to commuting and physical textbooks have decreased, there is an increased demand for high-speed internet and reliable digital devices, which can strain personal finances. These findings underscore the complex trade-offs between convenience, academic effectiveness, and financial burden in the transition to online education.