Average Time per Contact:

\\[ T_{\text{avg}} = \sum (P_i \cdot T_i) \\]

Base Effort per Friend:

\\[ E_{\text{base}} = F \cdot T_{\text{avg}} \\]

Total Effort:

\\[ E_{\text{total}} = N \cdot E_{\text{base}} \cdot D \cdot \left(1 – \frac{A}{A_{\text{max}}}\right) \\]

Effort Score:

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

Prioritization Strategy:

• Low Effort (\\( S < 20 \\)): Maintain all friendships.
• Moderate Effort (\\( 20 \leq S < 50 \\)): Prioritize close friends.
• High Effort (\\( 50 \leq S < 80 \\)): Reduce frequency or number of friends.
• Unsustainable (\\( S \geq 80 \\)): Significantly reduce effort or seek efficiency.

Where:

• \\( T_{\text{avg}} \\): Average time per contact (hours)
• \\( P_i \\): Proportion of interaction type \\( i \\) (%)
• \\( T_i \\): Time per contact for type \\( i \\) (hours)
• \\( E_{\text{base}} \\): Base effort per friend (hours/week)
• \\( F \\): Frequency of contact (contacts/week)
• \\( E_{\text{total}} \\): Total effort (hours/week)
• \\( N \\): Number of friends
• \\( D \\): Distance factor
• \\( A \\): Available time (hours/week)
• \\( A_{\text{max}} \\): Maximum available time (50 hours/week)
• \\( S \\): Effort score (%)

\\[ T_{\text{avg}} = (0.2 \cdot 0.5) + (0.7 \cdot 0.1) + (0.1 \cdot 2) = 0.1 + 0.07 + 0.2 = 0.37 \ \text{h} \\] \\[ E_{\text{base}} = 1 \cdot 0.37 = 0.37 \ \text{h/week} \\] \\[ E_{\text{total}} = 5 \cdot 0.37 \cdot 1.1 \cdot \left(1 – \frac{10}{50}\right) = 1.85 \cdot 1.1 \cdot 0.8 \approx 1.63 \ \text{h/week} \\] \\[ S = 100 \cdot \frac{1.63}{10} \approx 16.3 \ \% \\]

Strategy: Low Effort (Maintain all friendships)

\\[ T_{\text{avg}} = (0.1 \cdot 0.5) + (0.5 \cdot 0.1) + (0.4 \cdot 1.5) = 0.05 + 0.05 + 0.6 = 0.7 \ \text{h} \\] \\[ E_{\text{base}} = 3 \cdot 0.7 = 2.1 \ \text{h/week} \\] \\[ E_{\text{total}} = 15 \cdot 2.1 \cdot 1.0 \cdot \left(1 – \frac{30}{50}\right) = 31.5 \cdot 0.4 \approx 12.6 \ \text{h/week} \\] \\[ S = 100 \cdot \frac{12.6}{30} \approx 42.0 \ \% \\]

Strategy: Moderate Effort (Prioritize close friends)

\\[ T_{\text{avg}} = (0.4 \cdot 0.75) + (0.4 \cdot 0.15) + (0.2 \cdot 3) = 0.3 + 0.06 + 0.6 = 0.96 \ \text{h} \\] \\[ E_{\text{base}} = 2 \cdot 0.96 = 1.92 \ \text{h/week} \\] \\[ E_{\text{total}} = 8 \cdot 1.92 \cdot 1.5 \cdot \left(1 – \frac{15}{50}\right) = 15.36 \cdot 1.5 \cdot 0.7 \approx 16.13 \ \text{h/week} \\] \\[ S = 100 \cdot \frac{16.13}{15} \approx 100 \ \% \ (capped\ at\ 100) \\]

Strategy: Unsustainable (Significantly reduce effort or seek efficiency)