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QUESTION 21 (5 marks) This network shows the maximum number of supplies (in tonnes) that can be transported from a warehouse to a cyclone shelter along each road each day during an emergency. A 50 20 Warehouse Cyclone shelter 40 30 € a) Use the ‘maximum flow minimum cut’ theorem to determine the maximum amount of supplies that can reach the cyclone shelter each day. [3 marks] b) During a cyclone the intersection at vertex A is damaged and no longer allows for any supplies to pass through it. What is the new maximum amount of supplies each day that can reach the cyclone shelter? [2 marks]
QUESTION 7 Which cut (C; C C5or Cy) could be used to determine the maximum flow from the source to the sink in this network? Cnl C Z C\\3 C4 90 | Source Sink Not to scale (55 (A) C B) G C) G (D) C4
QUESTION 23 (4 marks) The network diagram shows the flow of water from the tank (source) to the kitchen tap (sink). L L L L Not to scale Tank ] D . 15 E a) Explain which dashed line (L L L; or L) 1s not a valid cut. [1 mark] b) Calculate the capacity of each dashed line that is a valid cut. [3 marks]
QUESTION 21 (4 marks) The road network shows the number of vehicles per hour travelling from the airport to the town centre. cut X _ College Airport Town centre \ Showground a) Determine the capacity of cut X. b) Determine the maximum flow from the airport to the town centre. [1 mark] [2 marks]
QUESTION 16 Determine the value of the cut made on the network diagram below. B 70 E<—Cut (A) 160 (B) 170 (C) 180 (D) 240
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