 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ib/paper-4/20h/b/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

The maximum flow is not unique. For any

x \in [1, 2]

f (S a) = f (a d) = 1, f (S b) = 3, f (S c) = f (ce) = 4,

and split the flow from

b

f (b d) = x, f (b e) = 3 - x .

f (d T) = 1 + x, f (e T) = 7 - x .

All capacities are respected precisely throughout the displayed interval, and every member of this one-parameter family has value

8

. For example,

x = 1

and

x = 2

give distinct maximum flows.

 New to topics? Read the docs here!