  In this paper we show that the so-called array Fr\'echet problem in
Probability/Statistics is (max, +)-linear. The upper bound of Fr\'echet is
obtained using simple arguments from residuation theory and lattice
distributivity. The lower bound is obtained as a loop invariant of a greedy
algorithm. The algorithm is based on the max-plus linearity of the Fr\'echet
problem and the Monge property of bivariate distribution.
