Solve small-scale practical problems involving flow networks (up to 8 possible cuts), including determining the minimum cut and the maximum flow.

The network diagram shows a distribution system where supplies are transported from a depot (source) to a relief centre (sink) along a series of roads. The numbers on each road represent the maximum capacity (in cases per hour) that can flow along that road in the direction shown. Use the maximum flow, minimum cut theorem to determine the maximum flow from the depot to the relief centre.

A logistics company transports goods from a distribution centre to a retail outlet. The network diagram below shows the maximum capacity (in tonnes per day) that can be transported along each route. Use the 'maximum flow, minimum cut' theorem to determine the maximum amount of goods that can reach the retail outlet each day.