Critical points and of polynomial functions

[cptstubing]

Homework Statement

A rectangular region of 125,000 sq ft is fenced off. A type of fencing costing $20 per foot was used along the back and front of the region. A fence costing $10 per foot was used for the other sides. What were the dimensions of the region that minimized the cost of the fence?

Homework Equations

A=l*w

The Attempt at a Solution

I haven't a clue where to begin with this. What should I be thinking?

 

[SammyS]

Homework Statement

A rectangular region of 125,000 sq ft is fenced off. A type of fencing costing $20 per foot was used along the back and front of the region. A fence costing $10 per foot was used for the other sides. What were the dimensions of the region that minimized the cost of the fence?

Homework Equations

A=l*w

The Attempt at a Solution

I haven't a clue where to begin with this. What should I be thinking?

Perimeter.

Think Perimeter.

 

[cptstubing]

Perimeter.

Think Perimeter.

I know this question should eventually look like a regular function like the practice questions I've been doing for ages, but I'm failing to see how I get there.

 

[SteamKing]

I know this question should eventually look like a regular function like the practice questions I've been doing for ages, but I'm failing to see how I get there.

What's the perimeter of a rectangle?

You have two dimensions to work with, length and width.

 

[cptstubing]

What's the perimeter of a rectangle?

You have two dimensions to work with, length and width.

L*W = area in sq feet, which is 125000.
But the variables, $20 and $10 per square foot of fence, don't seem relevant.
I don't see how I can get a perimeter from area=125000 and the price per foot of fence.
I do appreciate help with this.

 

[SteamKing]

L*W = area in sq feet, which is 125000.
But the variables, $20 and $10 per square foot of fence, don't seem relevant.
I don't see how I can get a perimeter from area=125000 and the price per foot of fence.
I do appreciate help with this.

For right now, forget about the area of the rectangle. That comes later.

If you have a rectangle, any rectangle, with a length L and a width W, what is the formula for the perimeter of this shape?

 

[cptstubing]

For right now, forget about the area of the rectangle. That comes later.

If you have a rectangle, any rectangle, with a length L and a width W, what is the formula for the perimeter of this shape?

Perimeter would be (L*2)+(W*2)

 

[Ray Vickson]

L*W = area in sq feet, which is 125000.
But the variables, $20 and $10 per square foot of fence, don't seem relevant.
I don't see how I can get a perimeter from area=125000 and the price per foot of fence.
I do appreciate help with this.

When you write L*W, what do you mean? What is L? What is W? So, if you did know L and W, what other aspects of the fencing could you compute using those values?

 

[cptstubing]

When you write L*W, what do you mean? What is L? What is W? So, if you did know L and W, what other aspects of the fencing could you compute using those values?

L*W means Area, or 125000. Length * Width. If I knew the two variables, I'd know the perimeter.

 

[Mark44]

L*W means Area, or 125000. Length * Width. If I knew the two variables, I'd know the perimeter.

You know the two variables -- L and W. You just don't happen to know their values. Even so, you should be able to write one expression that represents the perimeter of the fence, and another that represents the cost of that fence.

 

[cptstubing]

You know the two variables -- L and W. You just don't happen to know their values. Even so, you should be able to write one expression that represents the perimeter of the fence, and another that represents the cost of that fence.

P=(L*2)+(W*2)
Cost =(L*2*10)+(W*2*20)
I don't know if this is correct. What is I need to know before I can do this? A process or something?

 

[Mark44]

P=(L*2)+(W*2)
Cost =(L*2*10)+(W*2*20)
I don't know if this is correct.

That's a good start.

What is I need to know before I can do this? A process or something?

Forget process -- what you need to do is think about this problem.

You have another equation that involves the known area. Use it to solve for one of the variables in terms of the other. Then you can replace a variable in your cost equation, turning it into a function of a single variable.

 

[SammyS]

L*W = area in sq feet, which is 125000.
But the variables, $20 and $10 per square foot of fence, don't seem relevant.
I don't see how I can get a perimeter from area=125000 and the price per foot of fence.
I do appreciate help with this.

That's $20 and $10 per foot. It's not per square foot .

 

[Ray Vickson]

P=(L*2)+(W*2)
Cost =(L*2*10)+(W*2*20)
I don't know if this is correct. What is I need to know before I can do this? A process or something?

The farmer does not care about the perimeter; he just cares about the cost of fencing and the area enclosed. You know (that is, have expressions for) both of these in terms of L and W, so you are close to done. Can you see what to do next?