Answer:
7.86 km
Step-by-step explanation:
Let x represent the distance point P lies east of the refinery. (We assume this direction is downriver from the refinery.)
The cost of laying pipe to P from the refinery (in millions of $) will be ...
0.5√(1² +x²)
The cost of laying pipe under the river from P to the storage facility will be ...
1.0√(2² +(9-x)²) = √(85 -18x +x²)
We want to minimize the total cost c. That total cost is ...
c = 0.5√(x² +1) +√(x² -18x +85)
The minimum value is best found using technology. (Differentiating c with respect to x results in a messy radical equation that has no algebraic solution.) A graphing calculator shows it to be at about x ≈ 7.86 km.
Point P should be located about 7.86 km downriver from the refinery.
