Determine the capacity of a cut.

A water pipeline network flows from a treatment plant (vertex $P$) to three suburbs: North Bay ($N$), East Ridge ($E$), and South Valley ($S$), as shown in the network diagram below. The numbers on each edge represent the maximum flow capacity in megaliters per day. A cut is made at the set of edges that separate $P$ and its connected vertices from the remaining network. Determine the capacity of the cut that consists of the three edges connecting directly from $P$ to each suburb.

A logistics network distributes parcels from a distribution centre at vertex A to customers at vertex F. The diagram shows the maximum hourly capacity (in parcels) on each directed edge. A cut C is defined by separating vertices {A, B, D} from vertices {C, E, F}. (a) List all edges that cross cut C from the A-side to the F-side. [1 mark] (b) Determine the capacity of cut C. [2 marks]

A shipment delivery network connects a distribution centre to four regional warehouses via intermediate hubs. The diagram shows the maximum daily shipment capacity (in tonnes) on each route. Cut X is drawn across the network to separate the source from the destination hubs. (a) Identify all edges that cross cut X. [1] (b) Determine the capacity of cut X. [2]

Determine the capacity of cut X in the water distribution network shown.

A distribution network carries supplies from a central depot to a regional hub through an intermediate facility. The network is shown below, with capacity (in tonnes per day) marked on each directed edge. (a) Identify the edges that form cut Y (the edges that cross from the source side {S, A, B} to the destination side {C, D, T}). [1 mark] (b) Determine the capacity of cut Y by finding the sum of the capacities of the edges in the cut. [2 marks]

A supply chain network transports goods from a distribution centre at vertex A to a retail outlet at vertex F. The diagram shows the network with capacities (in pallets per hour) marked on each edge. A cut X separates the network into two regions: one containing vertices A, B, and C; the other containing vertices D, E, and F. Determine the capacity of cut X.

A communications company operates a network of data centres. The flow network shown represents the maximum daily data flow (in terabytes) between a central server S and a remote backup facility T. A cut is proposed at vertices {S, B, D}, separating these from {A, C, T}. (a) Identify all edges that cross the cut from the first set to the second set. (1 mark) (b) Determine the capacity of the cut. (2 marks)

A distribution network transports goods from a warehouse (vertex S) to a retail centre (vertex T). The edges show the daily capacity in tonnes. A cut X is drawn separating vertices {S, A, B} from vertices {C, D, T}. Determine the capacity of cut X.

A water distribution network supplies three towns from a central reservoir. The network diagram below shows the pipeline capacities (in kilolitres per hour) on each edge. A cut separates the reservoir from the towns and consists of the edges crossing from the source side to the towns side. Determine the total capacity of cut X, which includes the three pipelines crossing the cut.

A supply network transports emergency relief supplies from a depot to a disaster zone. The diagram shows the network with edges labelled by their daily capacity (in hundreds of kilograms). Which of the following correctly identifies the capacity of cut \'Y\', which separates the depot from the disaster zone?

A telecommunications network routes data from a central hub to a distribution centre. The network diagram shows the flow capacity (in Mbps) on each edge. Determine the capacity of the cut separating the hub from all paths leading towards the distribution centre.

A bottling facility distributes products to three regional warehouses via an intermediate distribution hub. The network diagram below shows the maximum flow capacity (in cartons per hour) on each route. A cut (X) is drawn to isolate the source from the destination vertices. Determine the capacity of cut X.

A logistics company operates a distribution network from a warehouse to multiple retail outlets. The network diagram below shows the maximum daily capacity (in tonnes) on each route. A cut has been made separating the warehouse from the retail outlets. What is the capacity of this cut?