User:CrZTgR/T.Fund

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Image:Return trip.png

d_{t_n} \ [or d_{u_m} \ ] the shortest or most efficient distance from S to Tn [or Um]
a_{t_n} \ [or a_{u_m} \ ] "on-site travel": distance(s) covered "around" Tn [or Um] point
b \ [or b_k \ ] distance covered between T1 and U1 [or k-th distance between some T and/or U points]
\sum_{i=1}^k b_i \ sum of all k distances covered between all T and U points
w_{t_n} \ [or w_{u_m} \ ] weight
r_{t_1} = 2d_{t_1}+a_{t_1} \ the shortest or most efficient return trip distance from S to T1
r_{t_1+u_1} = d_{t_1}+a_{t_1}+d_{u_1}+a_{u_1}+b \ combined return trip distance from S to T1 and U1 points
\begin{align}
r_{t_1-u_1} & = \frac {w_{t_1}(d_{t_1}+a_{t_1})r_{t_1+u_1}} {w_{t_1}(d_{t_1}+a_{t_1})+w_{u_1}(d_{u_1}+a_{u_1})} = \\
& = \frac {w_{t_1}(d_{t_1}+a_{t_1})(d_{t_1}+a_{t_1}+d_{u_1}+a_{u_1}+b)} {w_{t_1}(d_{t_1}+a_{t_1})+w_{u_1}(d_{u_1}+a_{u_1})} \\
\end{align} adjusted return trip distance from S to T1 (with U1 substracted)
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r_{t_n-u_n} =