Shortest path cont.
1) A company can put in the inventory 3 pieces of the merchandise at the maximum.
There is a contract to sell at the beginning of the 6th month all the pieces being in the
inventory at that time. “Now” we are at the beginning of the 1st month. Keeping one
piece on the inventory from one month to the next one costs kosztuje 10 $. In the
table bying and selling prices are given.
m.1
m.2
m.3
m.4
m.5
m.6
1 piece
280
280
295
305
305
500
2 piece
460
490
490
520
545
900
3 piece
740
765
785
820
850
1220
Buying price
2)
Connexions visible in the figure are given. Fill in the table so that it is known what to do if a
parcel comes to a city “row”: where to send it next and how much to charge (the payment is
equal to the number of kilometres to cover by the parcel). The parcel has to go each time using
the shortest path.
A
A
B
Selling
price
B
C
D
E
C
D
E
3) A tsar messenger has been sent form Moscow (1) to Irkuck (12). The weights of the arcs
(divided by 10) represent the probability that the messenger will safely leave the corresponding
arc. Find the path maximising the probability of getting to Irkuck. Remember that this means
maximising the multiplication of the arcs weights, thus the sum of their logarithms!