(Travelling Salesman)

1.         A salesman has to visit five different cities. The distance (in km) between the cities is given below. Find the sequence of the visit to these cities so that the distance he travels is minimum without visiting city more than once.

 To Cities From 1 2 3 4 5 1 – 70 60 80 40 2 70 80 50 60 3 60 80 – 90 70 4 80 50 90 – 70 5 40 60 70 80 –

(Ans. :  1 ® 5 ®  2 ® 4 ® 3 ®1 or 3 ® 4 ® 2 ® 5 ®1 are feasible routes which             give the same (300 kms) distance traveled. The salesman can take either     of these two routes.)

2.         A bread distribution Van of Santosh Bakery has to supply bread at different outlets. A, B and C in the morning. It collects the bread from Bakery and distributes to outlets A, B and C only once in the mornings. The van has to visit outlets A, B and C only once in the mornings. The van has to visit outlets once only and all the outlets have to be supplied with morning fresh bread. The distances of the outlets A, B and C from the Bakery is given in the following table. The van starts from Bakery and has to come back to the Bakery after visiting each outlet only once. Which route should be selected by the Van so that the total distance traveled by it is minimized. What is the total distance traveled by the Van ?

Find the alternate route, if any.

 From To Bakery Outlet A Outlet B Outlet C Bakery – 4 7 3 Outlet A 4 – 6 3 Outlet B 7 6 – 7 Outlet C 3 3 7 –

(Ans. :    BK ®  B ® A ® C ® BK

It has total distance of 7 + 6 + 3 + 3 = 19

There is also an alternate route

BK ® C ® A ® B ® BK

With a total distance 3 + 3 + 6 + 7 = 19.

These two routes are optimal.

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