I need help interpreting these results All of the math is do

I need help interpreting these results. All of the math is done, but if I can get some help writing up a report to the \"CEO\" about the most optimal path, and a clear drawing of the best path for the pipeline, that would be great! Thank you so much.

This is the part I need help with...

The U.S. Interior Secretary recently approved drilling of natural gas wells near Vemal, Utah. Your company has begun drilling and established a high-producing well on BLM ground. They now need to build a pipeline to get the natural gas to their refinery. While running the line directly to the refinery will be the least amount of pipe and shortest distance, it would require running the line across private ground and paying a right-of-way fee. There is a mountain directly east of the well that must be dri ed through in order to run the pipeline due east. Your company can build the pipeline around the private ground by going 1 mile directly west and then 5 miles south and finally 21 miles east to the refinery (see figure below). Cost for materials, labor and fees to run the pipeline across BLM ground is $300,000 per mile. For any pipeline run across private ground, your company incurs an additional $200,000 per mile cost for right-of- way fees. Cost of driling through the existing mountain would be $500,000 on top of the normal costs of the material, labor and fees for the pipeline itself. Also the BLM wi require an environmental impact study before allowing you to drill through the mountain. Cost for the study is estimated to be $100,000 and wil delay the project by 3 months costing the company another $50,000 per month. Your company has asked you to do the following: a) Determine the cost of running the pipeline strictly on BLM ground with two different scenarios: 1. heading east through the mountain and then south to the refinery 2. running west, south and then east to the refinery. b) Determine the cost of running the pipeline the shortest distance (straight line joining well to refinery across the private ground). c) Determine the cost function for this pipeline for the configuration involving running from the well across the private ground at some angle and intersecting the BLM ground to the south and then running east to the refinery. Use this function to determine the optimal place to run the pipeline to minimize cost. Clearly show all work including sketching the placement of the optimal pipeline. Make it very dlear how you use your knowledge of calculus to determine the optimal placement of the pipeline. Draw a graph of this cost function and label the point of minimum cost. 1 mile BLM Ground wel Private Ground 21 miles - BLM Ground refinery

Solution

Subject: Report about the most optimal path, and a clear drawing of the best path for the pipeline.

Hello Sir,

I have studied all the three different cases. Below all the calculations are given: (Include all your calculations with the diagrams in this report after each case.)

a) If we run strictly on BLM ground we encountered 2 different cases.

Case1.  If we head east through the mountain and then south to the refinery, the cost would be $8,250,000. The cost also include the charges of drilling the mountain, environmental study and the cost of project delay.

Case2. If we run west, south and then east to the refinery, the cost would be $8,100,000. In this case the pipe line would be 27 miles long.

b) If we run the pipeline on the shortest distance i.e. straight line joining the well to the refinery, the cost would be $10,310,000. Because the pipeline run 20.62 miles through the private ground only.

c) if we run the pipeline from the well across the private ground at some angle and intersecting the BLM ground to the south and then running east to the refinery, the cost would be $8,000,000. In this case we would run 6.25 miles on the private ground and 16.25 miles on the BLM ground.

By the calculations above it can be seen that running pipeline from the well across the private ground at some angle and intersecting the BLM ground to the south and then running east to the refinery will be the optimal path.