For functions g1,gt, we define the function max(g1,..., gt) via[max(g1, gt)\x) = max(g1(x)...

For functions g1,gt, we define the function max(g1,..., gt) via

[max(g1, gt)\x) = max(g1(x),gt(x)).

Consider the following problem. You are given n piecewise linear, continuous functions f1, fn defined over the interval [0, t] for some integer t. You are also given an integer B. You want to decide: Do there exist k of the functions fi1,...,fik so that

Prove that this problem is NP-complete.