Step 1 If x measures the distance from the point directly across the river from the storage tanks to the point P where the underwater pipe reaches the opposite shore, then there are m = 2 - X 2- 1 km of pipe over land and n = 1 +x- km of pipe underwater. refinery 2 storage tanks Step 2 We need to minimize the cost (measured in units of $100,000) of the pipeline, C(x) = 10 10 - 6 5 x + 10Vx2+ 1. step S We have 10x C'(x) = -5+ 10r V x2 + 1 Stap 4 Solving 0 = C'(x) leads to 51 x2 + 1 = 10x which can be re-written as x + 1 = 4x Step 5 Therefore, since x must be non-negative, we have V 3 Step 6 We must compare the costs for x = 0, 5. and 2. C(0) = 2 v 20 and C(2) = 10v5- step 7 Evaluate ( #3 ) = (10 - 1x V3 X X = 10 v3