Tutorial Exercise An oil refinery is located on the north bank of a straight river that is 1 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 5 km east of the refinery. The cost of laying pipe is $300,000/km over land to a point P on the north bank and $600,000/km under the river to the tanks. To minimize the cost of the pipeline, how far from the refinery should P be located? 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 = 5-x 5-km of pipe over land and n-1+2 refinery m km of pipe underwater. 22+1 storage tanks Step 2 We need to minimize the cost (measured in units of $100,000) of the pipeline, C(x)-15 15 3x+6√√x²+1. Step 3 We have бо C'(x)=-3+ +1 Step 4 Solving 0 C'(x) leads to which can be re-written as x²+1-42 Stop 5 Therefore, since x must be non-negative, we have 1 x= √3 Step 6 We must compare the costs for x 0, ✓ Step 7 Evaluate (+) (+)-(- 15- and 5. C(0) 21 21 and C(5) 6√26. 15 15+ √3 Step 8 Round your answer to two decimal places. The minimum of these costs occurs when x = and so P should be x km east of the refinery. Submit Skip (you cannot come back)