2025-267

The contractors for the new Alphaville Barão Geraldo luxury allotment have hired the brilliant students of the MO412 class to design a high-capacity water distribution network. The project's goal is to pump water from the campus lake (Node Lago) through a series of seven interconnected retention dams (Nodes A through G) to the development site (Node Alpha).

The contract specifies that the network must be able to deliver a minimum of 30,000 liters of water per minute. The students have produced the following design, with pipe capacities also measured in thousands of liters per minute:

Analyze the following propositions regarding the network's performance and limitations.

1. Suppose that, due to budget cuts, the pipe from Dam E to Dam G must be downgraded to a capacity of 5,000 L/min. With this hypothetical change, the contractual minimum delivery of 30,000 liters/minute would still be met.
2. To improve performance, a proposal is made to upgrade the pipe from Dam A to Dam D to a capacity of 18,000 L/min. This upgrade alone is sufficient to increase the network's total maximum flow.
3. If a critical failure shuts down the pipe from the Lago to Dam A (capacity becomes 0 L/min), the contractual minimum of 30,000 L/min can still be satisfied by rerouting flow through Dam B.
4. In the original, unmodified network, the pipe connecting Dam D to Dam F must operate at its full capacity of 5,000 L/min in order to achieve the maximum network flow.

Based on your analysis, choose the correct option:

1. Only proposition I is correct.
2. Only proposition II is correct.
3. Only propositions I, III, and IV are correct.
4. Only propositions II and III are correct.
5. None of the above

Original idea by: Eduardo Bouhid