Tuesday

September 30, 2014

September 30, 2014

Posted by **Katie** on Monday, November 17, 2008 at 7:23pm.

As the construction manager for the Lightem Up Power Company , you make decisions to hep minimize costs of the company's construction projects. Today you've been asked to determine the path of a pipe that will house communication lines from the factory to the power plant pictured here.

Factory . F_______7 miles_______

| river |

4 miles

|______________________|

.P Power

Plant

You must connect a pipe from point F at the factory to point P at the power plant. It will cost $12 per foot to lay the pipe on land and $21 per foot to lay the pipe in the water. Where should the pipe be placed so as to minimize the total cost of laying the pipe?

- Math -
**Reiny**, Monday, November 17, 2008 at 8:12pmlet the point directly across from P (the power plant) be Q.

then FQ = 7 miles

let R be a point between F and Q so that RQ = x miles, and FR = 7-x miles.

RP^2 = x^2 + 16

RP = (x^2+16)^(1/2)

So the path of the pipeline is PR + RF.

Cost of pipe on land: $12 per foot = $12(5280) per mile

= $63360 per mile

Cost of pipe in water: $21 per foot or

$110880 per mile

Cost = 110880*RP + 63360*FR

= 110880(x^2+16)^)1/2) + 63360(7-x)

d(Cost)/dx = (1/2)(2x)(110880)(x^2+16)^(-1/2) - 63360x

= 0 for a minimus of Cost

this reduced to

7x/√(x^2+16) = 4 (I divided by 15840x)

cross-multiplying and squaring both sides gave me

49x^2 = 16x^2 + 256

33x^2 = 256

x = 16/√33 = 2.785

then 7-x = 4.215

They should aim for a point 4.215 miles from the factory, then cross the river to the power plant.

**Answer this Question**

**Related Questions**

business - Direct verse indirect cost Estep Construction Company is composed of ...

Math - A company is planning to expand its business in a few years. New plant ...

Math - A company is planning to expand its business in a few years. New plant ...

Cost Accounting - Please somebody can help with the steps of this problem: Thank...

english - Which sentence uses correct parallel construction? A. Anyone who is ...

english - 7. Which sentence uses correct parallel construction? A. Most people ...

Physics - A fossil-fuel power plant that generates 1000MW of electrical power ...

phys - A town is planning on using the water flowing through a river at a rate ...

physics - A town is planning on using the water flowing through a river at a ...

physics - 1. You are planning to build a mini hydro power plant. A river near ...