A farmer wishes to fence oﬀ a rectangular patch in such a way that his barn ﬁts into the south–western corner with
its long side forming part of the southern boundary and its short side forming part of the western boundary. The
area of the part of the fenced oﬀ section not occupied by the barn is to be 8000 square metres. The barn has length
34 metres, width 24 metres. The cost of erecting the fence on the west side is 3 times the cost for the other sides.
If the enclosure is fenced at minimum cost what length of fencing is used?

Question

A farmer wishes to fence oﬀ a rectangular patch in such a way that his barn ﬁts into the south–western corner with
its long side forming part of the southern boundary and its short side forming part of the western boundary. The
area of the part of the fenced oﬀ section not occupied by the barn is to be 8000 square metres. The barn has length
34 metres, width 24 metres. The cost of erecting the fence on the west side is 3 times the cost for the other sides.
If the enclosure is fenced at minimum cost what length of fencing is used?