$($b$)$ Why does the red line exhibit a steeper slope when there are approximately $24$ hours of free time and a flatter slope when there are approximately $0$ hours of free time?

During the first few hours of studying, when the student is well$-$rested, productivity tends to be higher.

$$ As the student continues studying throughout the day, fatigue sets in$,$ leading to a decline in information retention. $q,$ Different levels of productivity can be observed depending on the number of hours of free time available for studying.

$$ Increasing the study time by an hour always results in an improvement in grades.

Students tend to adjust their daily free time based on their desired grade in the class and how much they value their leisure time.

$$ The red line represents the feasible frontier, but it does not account for performance enhancements resulting from learning over time.