Finding minimum cost using trig

missleannemarie

New member
Joined
Nov 13, 2016
Messages
1
A square plot of ground 100 feet on a side has vertices labeled A, B, C, D clockwise. Pipe is to be laid in a straight line from A to a point P on BC (P may be one of the vertices), and from there to point C. The cost of laying the pipe is $20 per foot if it goes through the lot (since if must be laid underground), and $10 per foot if it is laid along one of the sides of the square. What is the minimum cost for paying the pipe and how should the pipe be laid?
Solve this problem by a Trigonometric approach.

I already solved this problem using a rectangular approach. I found my cost function to be C(x)=20(sqrt(x2+10000))+10(100-x). I then found the derivative, set it zero, found the critical points within my domain, plugged that into my original function and found my desired value of x=57.73 as well as my minimum cost, $2732.05. But I have no idea how to do anything of that trigonometrically.
 
A square plot of ground 100 feet on a side has vertices labeled A, B, C, D clockwise. Pipe is to be laid in a straight line from A to a point P on BC (P may be one of the vertices), and from there to point C. The cost of laying the pipe is $20 per foot if it goes through the lot (since if must be laid underground), and $10 per foot if it is laid along one of the sides of the square. What is the minimum cost for paying the pipe and how should the pipe be laid?
Solve this problem by a Trigonometric approach.

I already solved this problem using a rectangular approach. I found my cost function to be C(x)=20(sqrt(x2+10000))+10(100-x). I then found the derivative, set it zero, found the critical points within my domain, plugged that into my original function and found my desired value of x=57.73 as well as my minimum cost, $2732.05. But I have no idea how to do anything of that trigonometrically.

First draw a sketch...
 
A square plot of ground 100 feet on a side has vertices labeled A, B, C, D clockwise. Pipe is to be laid in a straight line from A to a point P on BC (P may be one of the vertices), and from there to point C. The cost of laying the pipe is $20 per foot if it goes through the lot (since if must be laid underground), and $10 per foot if it is laid along one of the sides of the square. What is the minimum cost for paying the pipe and how should the pipe be laid?
Solve this problem by a Trigonometric approach.

I already solved this problem using a rectangular approach. I found my cost function to be C(x)=20(sqrt(x2+10000))+10(100-x). I then found the derivative, set it zero, found the critical points within my domain, plugged that into my original function and found my desired value of x=57.73 as well as my minimum cost, $2732.05. But I have no idea how to do anything of that trigonometrically.
I suspect the trig approach would be done by using angles and calculus. Just define one of the angles at A and go from there.
BTW, I think the approx answer is x=57.74.
 
Last edited:
Top