Introduction

Let us consider three markets P1, P2, P3 placed on an inclined plane (slope) with an angle α to the horizontal plane, denoted by (Sα). Assume that three cars transport products from (resp. to) a deposit P ∈ (Sα) to (resp. from) markets P1, P2, P3 ∈ (Sα) such that

• they always move in (Sα) along straight roads;

• the Earth's gravity acts on them (we omit other physical perturbations such as friction, air resistance, etc.);

• the transport costs coincide with the distance (we actually measure the time elapsed) from (resp. to) deposit P to (resp. from) markets Pi (i = 1, 2, 3).

We emphasize that usually the two distances, from the deposit to the markets and conversely, are not the same. The point here is that the travel speed depends heavily on both the slope of the terrain and the direction of travel. More precisely, if a car moves with a constant speed v (m/s) on a horizontal plane, it travels sin α cos θ meters in t seconds on (Sα), where θ is the angle between the straight road and the direct downhill road (θ is measured in a clockwise direction).