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Vernal Pipeline Project

Vernal Pipeline Project. Alexander Pham. Introduction. To whom it may concern, t he U.S. Interior Secretary has selected me to come up with the cheapest path to build a pipeline that will take the oil from where it was drilled to the refinery.

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Vernal Pipeline Project

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  1. Vernal Pipeline Project Alexander Pham

  2. Introduction • To whom it may concern, the U.S. Interior Secretary has selected me to come up with the cheapest path to build a pipeline that will take the oil from where it was drilled to the refinery. • I have come up with the costs of 5 (a,b,c,d,e) different possibilities.

  3. Option A Option A goes strictly through BLM ground only, which costs 500,000 dollars per every mile of pipeline made. $500,000 per mile x (4 miles + 12 miles + 36 miles) = $2,600,000

  4. Option B Option B goes directly west through the mountains, then it goes south straight to the refinery. Drilling through the mountain takes extra time and money. Drilling through the mountain will cost $2,000,000 along with the normal costs of the pipeline. There will also be an environmental study fee of $320,000. There will also be another $120,000 fee once a month for 4 months. $500,000 (32 miles +12 miles) + $2,000,000 mountain fee + $320,000 study fee + $120,000 (4 months) = $24,800,000

  5. Option C Option C goes straight through the private property at the extra cost of 350,000 dollars per mile on top the of the usual 500,000 dollar per mile pipeline. In order to figure out the length, I had to use the Pythagorean theorem. $500,000 (34.18 miles) + $350,000 (34.18 miles) = $29,053,000

  6. Option D Option D goes through both private ground and BLM ground. It goes straight south from the refinery through the private land and from there it goes east to the refinery. $500,000 (12 miles south + 32 miles east) + $350,000 (12 miles) = $26,200,000

  7. Option E Option E is the best choice, and I will show you why. The pipeline will be built going diagonally south east going through the private ground. Once it gets to the BLM ground, it will start heading straight east to the refinery. In order to find the length in miles that we have to go south east for, we have to a do a little bit of math, so bear with me. To find the length of Y, we have to use the Pythagorean theorem again. We have to remember that Y is going to cost us $850,000 per mile because it is going through private property, and the length (32-x) will cost us $500,000 dollars because it is just going through BLM land. So our cost equation is as follows: (y) C(x)= Now we have to minimize this function. In order to do that, we have to take the derivative of our cost function and set it equal to zero. This will give us the minimum x-value. (see next slide)

  8. Now that we know X, we can figure out what Y is equal to by plugging x into the previous Pythagorean equation. Option E (continued) We can now put this into our original cost function to figure out how much this will cost. 𝑪(𝒙) = $𝟐𝟒,𝟐𝟒𝟗,𝟎𝟎𝟎 This is the cheapest pipeline pathway!

  9. Reflection We have learned many different things in Calculus that can be used to solve everyday issues such as the one above. There is a large array of problems that calculus can be used to solve. The field I want to go into is pharmacy and the pharmacist I work with says he actually used differentials in pharmacy school; for example, they use calculus to find out what medicine can be used at the same time as other ones, because some taken at the same time can be very dangerous.

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