Building a Pipeline Optimization Problem (Please Help!)

[ardentmed]

Hey guys,


I'm having trouble with this problem set I'm working on at the moment. I'd appreciate some help with this question:

(I'm only asking about number two. Ignore number one please.)

So if the length for the hypotenuse of the leftmost triangle is represented by:
c^2 = x^2 + y^2

Then,

c= √(2500 + x^2)

Therefore, the total cost comes to:

C(x) = 400,000-20,000x + 50,000√(2500 + x^2)

Am I on the right track?

Moreover, we need to optimize and deduce the minimum cost, x's smallest possible value:

c'(x) = dy/dx (400,000-20,000x + 50,000√(2500 + x^2))

Then isolate and solve for "x."

x=21.821789 km

x ~ 21.km.




Thanks in advance.

 

[HallsofIvy]

Hey guys,


I'm having trouble with this problem set I'm working on at the moment. I'd appreciate some help with this question:

(I'm only asking about number two. Ignore number one please.)

So if the length for the hypotenuse of the leftmost triangle is represented by:
c^2 = x^2 + y^2

Then,

c= √(2500 + x^2)

Therefore, the total cost comes to:

C(x) = 400,000-20,000x + 50,000√(2500 + x^2)

[/FONTAm I on the right track?

Yes, that is the correct cost formula.

Moreover, we need to optimize and deduce the minimum cost, x's smallest possible value:

c'(x) = dy/dx (400,000-20,000x + 50,000√(2500 + x^2))

This is bad notation. The derivative is "dy/dx" where y is whatever function you are differentiating. Since you are calling the function "c", you should have either "dc/dx" or c'(x) = d(400,000-20,000x + 50,000√(2500 + x^2))/dx. There is no "y" in this problem.

Then isolate and solve for "x."

x=21.821789 km

x ~ 21.km.




Thanks in advance.

What you say you were going to do is correct but you have left out all the work! What did you get for c'? How did you solve for x?

 

[ardentmed]

Yes, that is the correct cost formula.


This is bad notation. The derivative is "dy/dx" where y is whatever function you are differentiating. Since you are calling the function "c", you should have either "dc/dx" or c'(x) = d(400,000-20,000x + 50,000√(2500 + x^2))/dx. There is no "y" in this problem.


What you say you were going to do is correct but you have left out all the work! What did you get for c'? How did you solve for x?

When solving for f'(c)=0, I computed:

-40,000√(x^2 +2500) +100,000x = 0

And then I isolated x and computed x=21.8km.

Am I close?

Thanks in advance.

 

[ardentmed]

I'm still at a loss as to what to do next. Any help, guys?

Thanks again.

 

[HallsofIvy]

That looks correct to me. Although, you listed the answer initially as "21 km". If you are rounding to the nearest km, I would have said 22 km.

 

[ardentmed]

That looks correct to me. Although, you listed the answer initially as "21 km". If you are rounding to the nearest km, I would have said 22 km.

Is 21.8km accurate for significant figures, or should I stick with 22km since the questions uses 50km as one of the values (two significant figures).

Thanks again.

 

[Deleted member 4993]

Is 21.8km accurate for significant figures, or should I stick with 22km since the questions uses 50km as one of the values (two significant figures).

Thanks again.

50 km has only one significant figure - however, 50. km has two significant figure.

For this problem, I would expect 21.8 km to be the expected correct answer.