# Question: min 6w12 5w13 7w23 4w24 3w34...

###### Question details

min 6w_{12} + 5w_{13} + 7w_{23} +
4w_{24} + 3w_{34} + 2w_{35} +
8w_{45}

subject to

u1 - u2 <= w12

u1 - u3 <= w13

u2 - u3 <= w23

u2 - u4 <= w24

u3 - u4 <= w34

u3 - u5 <= w35

u4 - u5 <= w45

u1 - u5 >= 1

w_{ij} >= 0

This problem is the dual of a graph optimization problem. State which problem it is, draw the graph. Find by inspection the optimal solutions to both primal and dual problems.