Question 3 - Calculus & Network Flow

In the Ford–Fulkerson method, the bottleneck capacity of an augmenting path is usually defined as the minimum of the residual capacities of its edges. Suppose a path has two edges whose residual capacities vary with time \(t\), \(r_1(t) = t^2 + 1\) and \(r_2(t) = e^t\).

Instead of taking the minimum, define the augmenting path capacity as the average of the residuals: \(R(t) = \frac{r_1(t) + r_2(t)}{2}\).

What is the derivative \(\frac{dR}{dt}\) at \(t = 1\)?
A) 1
B) 2.34
C) 2.72
D) 2.86
E) None of the above
Original idea by: Jhonatan Cléto

Comentários

  1. Joao Meidanis29 de setembro de 2025 às 01:21

    Boa questão, mas mistura Ford-Fulkerson de forma um pouco artificial. Quanto à parte de cálculo, é facinha.

    ResponderExcluir

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