The Daltons has an escape plan from prison. They will go through tunnel but they

Question

The Daltons has an escape plan from prison. They will go through tunnel but they have only 17 minutes in order to not be captured by guards. The tunnel is so dark and they have only one flashlight. A maximum of two people can cross from the tunnel at one time. Any party who crosses, either 1 or 2 people, must have the flashlight with them. The flashlight must be walked back and forth; it cannot be thrown or returned in any other way. Each 4 brothers has a different speed as follows:
Joe
1 minute
William
2 minute
Jack
5 minute
Averell
10 minute
A pair must move together at the rate of the slower brother’s pace. For example, if Joe Dalton and Averell Dalton walk across first, it will take them 10 minutes to get to the other side of the tunnel. If Averell then returns with the flashlight, a total of 20 minutes will have passed and they have failed the mission. You must show how to get the brothers cross from the tunnel in time to escape from prison. Use dynamic programming to find a strategy. (Hint: see how the dynamic programming is used for travelling salesperson problem)

Explanation / Answer

According to me the minimum time will be 19 minutes.

Suppose firstly Averell and joe goes then they will take 10 min and one of them have to come (because of torch) so joe will come s total time is 11 min. Now joe and jack goes and it will take 5 min. and joe will come so total time is, 11+5+1,17min (Now guards will catch them). Now joe and william goes and they will take 2min.. So minimum time for these brothers to cross this tunnel will be 19mins.

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