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