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We consider a simplified model of first-passage percolation, involving twofamilies of i.i.d. random variables $\{\xi_{ij}\}$ and $\{\eta_{ij}\}$corresponding to the weights of the horizontal and vertical edges respectively.We obtain an explicit formula for the limiting shape of the first-passagedistance expressed in terms of the corresponding limit shapes of the two setsof weights for the Sepp\"al\"ainen--Johansson model. We also study the limitingfluctuations of this model when at least one of the sets of weights isBernoulli distributed.

Limit shape formulas for a generalized Sepp\"al\"ainen-Johansson model