Find minimal time for four people crossing

Assume there are four people who need to cross a narrow bridge at night using a single flashlight.

• Each person $i$ requires a different, known amount of time $t_i$ to cross the bridge when walking alone.
• At most two people can be on the bridge at the same time.
• Whenever one or two people cross, they must carry the flashlight with them.
• If two people cross together, the time for that crossing is the maximum of their two individual times (they must move at the speed of the slower person).
• The flashlight cannot be thrown or sent by any means other than being carried by a person walking back across the bridge.

You are given the four crossing times $t_1, t_2, t_3, t_4$ (positive integers). You may assume, without loss of generality, that they are sorted so that

$t_1 \le t_2 \le t_3 \le t_4.$

Tasks:

1. Determine a strategy (sequence of crossings and returns) that minimizes the total time required for all four people to end up on the other side of the bridge with the flashlight.
2. Express the minimal total time in terms of $t_1, t_2, t_3, t_4$ and clearly describe the order in which people cross and who returns with the flashlight.

Do not write code; just provide the final minimal total time and explain your reasoning and crossing sequence step by step.