1. Bree Gray Math 1210 Fall Semester

2.  Your company wants to run a pipeline from the well to the refinery. You are to propose the most cost effective way to build this pipeline.

3.  $300,000 per mile for material, labor, and fees  $200,000 per mile if on private land  $500,000 to drill through mountain  $100,000 to do environmental study  $50,000 per month for any delays

4.  Head east through mountain and south to the refinery. 20 miles 5 miles

5.  20 miles east+5 miles south=25 total miles  25 miles x $300,000/mile=$7,500,000  Additional costs: $500,000 for drilling, $100,000 for environmental study, $150,000 for 3 month set back  Total cost: $8,250,000

6.  Run the pipeline west, south, and then east

7.  1 mi west+5 mi south+21 mi east=27 miles  27 miles x $300,000/mile=$8,100,000  This is cheaper than option 1.

8.  Running the shortest distance through private ground. X 20 miles 5 miles

9.  Solve for x using Pythagorean Theorem  √400+25=20.6155 miles  20.616 miles x $500,000= $10,307,764.06  More expensive than both previous options.

10.  A pipeline that runs southeast on private property and goes through the south boarder of the private property and then heads east to the refinery. X C a α β

11.  a=20-x so C= √25+(20-x)²  $500,000 √25+(20-x)²)+$300,000x  Cost’(x)=$250,000(-2(20-x))(25+(20-x) ²)^- ½+$300,000  Simplify:

12.  u ²=14.0625 so u=3.75  20-x=3.75 and x=16.25  f’(16.25)=250000(25+(20-16.25)²)^-½+300000  Total cost: $800,000  This is the cheapest option

13.  C= √25+14.0625=6.25 miles through private ground  α=tan(3.75/5)=36.87°  β =|cos(3.75/6.25)-180|=126.87° X C a α β