An engineer is designing a pipeline which is supposed to connect two points $P$ and $S.$ The engineer decides

to do it in three sections. The first section runs from point $P$ to point $Q,$ and costs $$44$ per mile to lay, the

second section runs from point $Q$ to point $R$ and costs $$54$ per mile, the third runs from point $R$ to point $S$

and costs $$38$ per mile. Looking at the diagram below, you see that if you know the lengths marked $x$ and $y,$

then you know the positions of $Q$ and $R.$ Find the values of $x$ and $y$ which minimize the cost of the pipeline.

Please show your answers to $4$ decimal places.