Need explaination of each step and desmos graph please.
Calculus I Signature Assignment
Rough Draft Due (Parts 1 & 2): February 19th (MWF) and February 20th (TTh)
Final Assignment Due: April 13th (MWF) and April 14th (TTh)
Permission Granted from Salt Lake CC by Suzanne Mozdy for use of their Pipeline Problem (July 2018)
The U.S. Interior Secretary recently approved drilling of natural gas wells near Vernal, Utah. Your company has begun drilling and established a high-producing well on the Bureau of Land Management (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 west 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 15 miles south and 45 miles west to the refinery (see figure above). Cost for materials, labor and fees to run the pipeline across BLM ground is $350,000 per mile.
Cost of drilling through the existing mountain would be a one-time cost of $5,800,000 on top of the BLM ground costs ($350,000 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 $150,000 and will delay the project by 6 months costing the company another $78,000 per month.
For any pipeline run across private ground, your company incurs an additional $110,000 per mile cost, for right-of-way fees, on top of the BLM ground costs ($350,000 per mile) of the pipeline itself.
Your company has asked you to look at the different possible pathways to determine the most cost efficient. Create a presentation of your finding to submit to your company’s CEO and other superiors.
Part 1: BLM Ground Determine the cost of running the pipeline strictly on BLM ground with two different cases:
One running south and then west to the refinery.
One heading west, through the mountain, and then south to the refinery.
Part2: Shortest Distance Determine the cost of running the pipeline:
The shortest distance across the private ground to the refinery.
West to the mountain, straight south across private ground, and then straight west to the refinery.
You can turn the assignment in at this point to get feedback on your work and the format. The rough draft will be accepted if it is a fully completed and type submission on February 19th (MWF) or February 20th (TTh).
Part3: Minimizing Cost 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 west to the refinery.
Use this function to find the optimal way to run the pipeline to minimize cost. Determine the following…
The length of pipe that runs across private land.
The length of the pipe that runs on BLM land.
The angle at which your optimal path leaves the well (angle of depression).
Clearly show all work including drawing the pipeline on the figure above. Make it very clear how you use your knowledge of calculus to determine the optimal placement of the pipeline.
Include a computer generated graph of the optimal cost function, “C(x)”, for this pipeline for any configuration involving crossing some private ground as well as some BLM ground. Make sure to use the correct domain of the function to scale your axes appropriately and to label the minimum point.
Part 4: Reflection Write at least one paragraph to address the following questions.
Putting aside the cost of each pathway, if you had to make a decision as to which pathway to construct, which one would you choose and why?
How did this assignment help you to understand the importance of cost of construction?
An introduction slide. This should contain an organized list of all given information.
One slide devoted to each possible path. Each slide should include
Diagram of the pathway requested.
Important steps for math used to make determinations
A brief explanation of the steps.
The total number of miles the pipeline will cover.
Cost of the pipeline.
A reflection slide.
Important mathematical steps will be shown and will be correct (Ex. To find the length of the pipeline across the private ground, I used the Pythagorean Theorem length of the hypotenuse.)
All equations and formulas will be created using an Equation Editor or Math Type.
Use exact values, rounding costs to the nearest cent only after the final calculation.
Any variables you use will be clearly defined and shown in your diagrams
The cost function graph will be accurately generated using mathematical software, i.e. Desmos.
A word-processed explanatory narrative with correct spelling and grammar will allow the reader to follow your process. Hand-written work will not be graded
Your report should be an exposition of your finest work and presentation.
