An engineer is designing a pipeline which is supposed to connect two points P and S. The engineer decides to do it in th

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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
$40 a mile to lay, the second section runs from point Q to point R
and costs $50 mile , the third runs from point R to point S and
costs $38 a 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.



x = miles

y = miles