A weighted graph $G= (V, E, W_1, W_2)$ has two cost functions $W_1, W_2 : E \rightarrow \mathbb{R}$. Each edge $e$ has two costs $W_1(e)$ and $W_2(e)$. We may think the costs as representing different resources, such as time and fuel. Similarly, a path $p =e_1, e_2, \dots e_n$ has two costs,
$$W_1(p) = \sum_i W_1(e_i) \qquad \text{and} \qquad W_2(p) = \sum_i W_2(e_i) \qquad$$
Consider the following decision problem: given two nodes $u, v \in V$ and two constants $c_1, c_2$, does there exist a path $p$ from $u$ to $v$ such that $W_1(p) \le c_1$ and $W_2(p) \le c_2$?
Is it NP complete or is a polynomial algorithm known to exist?