The U.S. Interior Secretary recently approved drilling of natural gas wells near Vernal, Utalh 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 drilled through in order to run the pipeline due east. Your company can build the pipeline around the private ground by going 6 miles directly west and then 15 miles south and finally 28 miles east to the refinery (see figure below). Cost for materials, labor and fees to run the pipeline across BLM ground is $320,000 per mile Cost of drilling through the existing mountain would be a one-time cost of $4,400,000 on top of the normal costs ($320,000 per mile) of the pipeline itself. Also the BLM will require an environmental impact study before allowing you to drill through the mountain. Cost for the study is estimated to be $200,000 and will delay the project by 8 months costing the company another $85,000 per month For any pipeline run across private ground, your company incurs an additional $90,000 per mile cost for right-of-way fees Your company has asked you to do the following a) Determine the cost of running the pipeline strictly on BLM ground with two different cases i)One running west, south and then east to the refinery i) One heading east through the mountain and then south to the refinery b) Determine the cost of running the pipeline i) The shortest distance across the private ground to the refinery i)Straight south across the private ground, then straight east to the refinery c) Determine the cost function for the 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 find the optimal way to run the pipeline to minimize cost. Determine the length of pipe that runs across private land and how far from the refinery it starts running on BLM land. Determine the angle at which your optimal path leaves the well. Clearly show all work including drawing the pipeline on the figure below. Make it very clear how you use your knowledge of calculus to determine the optimal placement of the pipeline