Question 125
On the bank of a river $100$ meters wide is an electrical plant and on the opposite bank, and $500$ meters upstream, a factory is being built. Knowing that the river is rectilinear between the plant and the factory, that the laying of cables along the shore costs $9\,€$ each meter and that the laying of cables on the water costs to $15\,€$ Each meter, what is the most economical length possible between the power plant and the factory?