Study Session Planner

Subject Priority Weight:

\\[ W_i = P_i \\]

Total Weight:

\\[ W_{\text{total}} = \sum W_i \\]

Allocated Time per Subject:

\\[ T_i = A \cdot \frac{W_i}{W_{\text{total}}} \\]

Number of Sessions per Subject:

\\[ S_i = \text{ceil}\left( \frac{T_i}{L} \right) \\]

Productivity Score:

\\[ S = \min\left(100 \cdot \frac{A}{A_{\text{max}}}, 100\right) \\]

Where:

• \\( W_i \\): Weight for subject \\( i \\) (Low: 1, Medium: 2, High: 3)
• \\( W_{\text{total}} \\): Sum of weights
• \\( T_i \\): Study time for subject \\( i \\) (hours/day)
• \\( A \\): Total daily study time (hours/day)
• \\( S_i \\): Number of sessions for subject \\( i \\)
• \\( L \\): Preferred session length (hours)
• \\( S \\): Productivity score (%)
• \\( A_{\text{max}} \\): Maximum study time (8 hours/day)

\\[ W_{\text{Math}} = 3, \quad W_{\text{English}} = 1 \\] \\[ W_{\text{total}} = 3 + 1 = 4 \\] \\[ T_{\text{Math}} = 2 \cdot \frac{3}{4} = 1.5 \ \text{h}, \quad T_{\text{English}} = 2 \cdot \frac{1}{4} = 0.5 \ \text{h} \\] \\[ S_{\text{Math}} = \text{ceil}\left( \frac{1.5}{1} \right) = 2, \quad S_{\text{English}} = \text{ceil}\left( \frac{0.5}{1} \right) = 1 \\] \\[ S = 100 \cdot \frac{2}{8} = 25 \ \% \\]

Schedule: 08:00 AM–09:00 AM (Math), 09:10 AM–10:10 AM (Math), 10:20 AM–11:20 AM (English)

\\[ W_{\text{Math}} = 3, \quad W_{\text{Physics}} = 2, \quad W_{\text{History}} = 1 \\] \\[ W_{\text{total}} = 3 + 2 + 1 = 6 \\] \\[ T_{\text{Math}} = 4 \cdot \frac{3}{6} = 2 \ \text{h}, \quad T_{\text{Physics}} = 4 \cdot \frac{2}{6} \approx 1.33 \ \text{h}, \quad T_{\text{History}} = 4 \cdot \frac{1}{6} \approx 0.67 \ \text{h} \\] \\[ S_{\text{Math}} = \text{ceil}\left( \frac{2}{1} \right) = 2, \quad S_{\text{Physics}} = \text{ceil}\left( \frac{1.33}{1} \right) = 2, \quad S_{\text{History}} = \text{ceil}\left( \frac{0.67}{1} \right) = 1 \\] \\[ S = 100 \cdot \frac{4}{8} = 50 \ \% \\]

Schedule: 09:00 AM–10:00 AM (Math), 10:10 AM–11:10 AM (Math), 11:20 AM–12:20 PM (Physics), 12:30 PM–01:30 PM (Physics), 01:40 PM–02:40 PM (History)

\\[ W_{\text{Math}} = 3, \quad W_{\text{Physics}} = 3, \quad W_{\text{Chemistry}} = 2, \quad W_{\text{Biology}} = 2, \quad W_{\text{English}} = 1 \\] \\[ W_{\text{total}} = 3 + 3 + 2 + 2 + 1 = 11 \\] \\[ T_{\text{Math}} = 6 \cdot \frac{3}{11} \approx 1.64 \ \text{h}, \quad T_{\text{Physics}} = 1.64 \ \text{h}, \quad T_{\text{Chemistry}} = 6 \cdot \frac{2}{11} \approx 1.09 \ \text{h} \\] \\[ T_{\text{Biology}} = 1.09 \ \text{h}, \quad T_{\text{English}} = 6 \cdot \frac{1}{11} \approx 0.55 \ \text{h} \\] \\[ S_{\text{Math}} = \text{ceil}\left( \frac{1.64}{0.5} \right) = 4, \quad S_{\text{Physics}} = 4, \quad S_{\text{Chemistry}} = \text{ceil}\left( \frac{1.09}{0.5} \right) = 3 \\] \\[ S_{\text{Biology}} = 3, \quad S_{\text{English}} = \text{ceil}\left( \frac{0.55}{0.5} \right) = 2 \\] \\[ S = 100 \cdot \frac{6}{8} = 75 \ \% \\]

Schedule: 07:00 AM–07:30 AM (Math), 07:40 AM–08:10 AM (Math), 08:20 AM–08:50 AM (Math), 09:00 AM–09:30 AM (Math), 09:40 AM–10:10 AM (Physics), 10:20 AM–10:50 AM (Physics), 11:00 AM–11:30 AM (Physics), 11:40 AM–12:10 PM (Physics), 12:20 PM–12:50 PM (Chemistry), 01:00 PM–01:30 PM (Chemistry), 01:40 PM–02:10 PM (Chemistry), 02:20 PM–02:50 PM (Biology), 03:00 PM–03:30 PM (Biology), 03:40 PM–04:10 PM (Biology), 04:20 PM–04:50 PM (English), 05:00 PM–05:30 PM (English)