GAS PIPELINE VIDEOBree Gray Math 1210 Fall

Semester

Problem

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.

Costs

$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

Option 1

Head east through mountain and south to the refinery.

20 miles

5 miles

Math of Option 1

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

Option 2

Run the pipeline west, south, and then east

Math of Option 2

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.

Option 3

Running the shortest distance through private ground.

X

20 miles

5 miles

Math for Option 3

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.

Option 4

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

Math for Option 4

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:

2

22

2

160000022200000

2500000)25(900000

300000)20(25

))20(2(250000

u

uu

x

x

Math for Option 4 (cont.)

u²=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

Finish solving for Option 4

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