SLCC Math 1210 Pipeline Project Spring 2015

Transcription

1 SLCC Math 1210 Pipeline Project Spring 2015 Dear CEO, In response to your request for providing a cost efficient method in constructing a pipeline from the natural gas wells to the refinery near Vernal, Utah, the Calculus Team has formulated the following analysis. In this report you will find five different scenarios that address the pipeline project, and a recommendation of the most cost efficient method is provided herein. Scenario 1: BLM Land As illustrated below, the pipeline for Scenario 1 would run west 5 miles, turn south 15 miles, and east 45 miles to the refinery. The total mileage for the route would be 65 miles. The pipeline would be constructed strictly on BLM land and would cost $500K to construct. The total cost for Scenario 1 is $32.5M. C (x) = 65($500, 000) = $ 32, 500, 000 Scenario 2: Mountain Corridor In Scenario 2 the pipeline would run 40 miles directly east through mountains, and 15 miles south to refinery, totaling 55 miles. The pipeline would be built on BLM land and would cost $500K per mile. The cost of drilling through the mountain would result in a one-time cost of $3.5M. The mountain pipeline would also require an environmental study that would cost $420K, and will delay the project for 6 months resulting in $1,080K in an additional costs. The total cost for Scenario 2 is $32.5M. C (x) = 55($500, 000) + $ 3, 500, $ 420, ($1, 080, 000) = $ 32, 500, 000

2 Scenario 3: Cross Private Ground The pipeline in Scenario 3 would directly cross private property for 42.7 miles from wells to the refinery. The cost of construction is $500K per mile plus an additional $350K per mile for right-of-way fees. Although this may the shortest route the cost for the project is projected to be $36.3M. C (x) = 42.72($850, 000) = $ 36, 312, 000 Scenario 4: BLM and Private Land In Scenario 4, the pipeline would run 15 south through private land, and 40 miles east on BLM land. Construction costs would be $500K per mile on BLM land and $850K per mile on private land. The total cost for Scenario 4 is $32.75M. C (x) = 15($850, 000) + 40($500, 00) = $ 32, 750, 000 Scenario 5: Optimization The optimal cost is described in Scenario 5. As illustrated in the picture below, shows the pipeline cutting through private land for 18.5 miles in a southeast direction. Once reaching BLM land the pipeline would head due east for 29.1 miles to the refinery. The total cost for this scenario is $30.3M, making it the most efficient pipeline scenario for the project. To prove that this is the most cost efficient scenario

3 C (x) = $ 850, 000( x ) + $ 500, 000(40 x ) To identify the most cost efficient path for the pipeline, the derivative of the cost function must be taken. The steps of the finding the derivative are shown below. C(x)= 850k (x^2+225)^(½) + 500k (40 x) = 850k (x^2+225)^(½) + 2,000k 500k(x) C (x)= 850k (½)(x^2+225)^( ½) (2x) 500k = (850k(x)/ x ) 500k After taking the derivative, the equation is set equal to zero to find the x-intercept. This will pinpoint the value of x, and determine construction costs on the pipeline. C (x) = 850x x = 0 850x 722,500x = , x = x x +225 x ,225x 2 = 2, 500 7, 225x 2 = 2, 500x , 500 x , 725x 2 = 562, 500 x 2 = x =

4 Figure 1 shows the graph of the cost function of Scenario 5. The vertex of the functions shows the quadrants for the cost function is ( , $30,310). This minimum is consistent with the result that was found in the previous calculation. Figure 1: Graph of C(x) Figure 2 is the graph of the First Derivative test which validates the findings that is the critical point for the function

5 Figure 2: First Derivative Test of C (x) In closing, it is recommended that Scenario 5 will provide the most cost efficient method in constructing the pipeline. By constructing Scenario 5, Natural Gas, Inc. will save more than $2.2M in construction costs, and will complete the pipeline in a timely manner. This will ultimately result in generating cash flow to Natural Gas, Inc. and expedite the return on investment for the construction of the pipeline. Sincerely, Amber, Chase, and Zach Reflection Essay

6 A subject has power when it can be applied outside of the classroom, and for us calculus has done that. Calculus has not been the easiest math class any of us has ever taken. But as we approach the end of the semester it is easy to see how powerful a tool calculus can be when applied to solving real world problems. Calculus is a very useful subject that can be applied to many different fields of study and occupations. The obvious application is to engineers. Whether it is constructing a pipeline as mentioned above, or determining the most efficient gas mileage for a new car, calculus is key. Physics is another area where calculus can be applied. By finding derivatives the velocity and acceleration of an object can be found to pinpoint critical points in time. Finally, economics and business is another area where calculus can be applied. Derivatives can be used to find profit maximization points, identify areas to minimize costs, and overall help business leaders make good business decisions. One area that calculus can very useful is in business. One person in our group is interested in business analytics. This field is becoming more important as the business world becomes more complex. Calculus can help solve problems that many companies are facing. Whether it be finding the optimal payroll level for store employees, or identify how many units of a certain product to buy, calculus is useful. Another group member is interested in forestry and environmental studies. As climates and weather patterns change, calculus can be used to determine the rate of change in habitats and ecosystems. This can help identify how many trees to plant a year to replenish forests, the optimal level of hunting licenses to be issued, etc. In closing, the big take away from taking this course is the way that calculus makes you think. It changes the way that you look at the world. This is the true value of calculus. It challenges the way you think and solve real life problems. Unfortunately, this is a concept that is not taught in many courses on campus.