Question
stumped on this
Building a Pipeline An oil company wishes to construct a pipeline from us offshore facility A to its refinery B. The offshore facility is 2 miles from shore, and refinery is 1 mile inland. Furthermore, A and B are 5 miles apart, as shown in the figure. The cost of building the pipeline is S3 million per mile in the water, and $4 million per mile on land So, the cost of the pipeline depends on the location of point P, where it meets the shore. What would lie the most economical route of the pipeline Imagine that you arc to write a report to the oil company about this problem. Let x be the distance shown m the figure. Determine the cost of building the pipeline from A to P, and the cost from P to B. Analyze some sample pipeline routes and their corresponding costs. For instances, what is the cost of the most direct route? Then use calculus to determine the route of the pipeline that minimizes the cost. Explain all steps of your development and include any relevant graphs.
Explanation / Answer
total cost of pipeline would be 3(4+x^2)^0.5+4*(22+x^2-9.16x)^0.5 for this to be min differentiate whole term and equate it to 0 then we get optimam value of x=1.877 meters and total cost =19.75 million dollars
