Lay the pipeline as shown in the above picture.

Suppose: Point P is located at the downstream x(km) of the refinery, and 0≤x≤ 10. The total cost of laying is y billion yuan.

According to the meaning and known, there are:

y=4x+6√[2.5？ +( 10-x)？ ]

y=4x+6√(x？ -20x+ 106.25)

y'=4+3(2x-20)/√(x？ -20x+ 106.25)

y'=[4√(x？ -20x+ 106.25)+6x-60]/√(x？ -20x+ 106.25)

1, sequence: y' > 0, namely: [4√(x? -20x+ 106.25)+6x-60]/√(x？ -20x+ 106.25)>0

Yes: 2√(x? -20x+ 106.25)+3x-30>0

30-3x