# Critical points and of polynomial functions

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1. Apr 14, 2015

### cptstubing

• Member warned about posting with no effort
1. The problem statement, all variables and given/known data
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?

2. Relevant equations
A=l*w

3. The attempt at a solution
I haven't a clue where to begin with this. What should I be thinking?

2. Apr 14, 2015

### SammyS

Staff Emeritus
Perimeter.

Think Perimeter.

3. Apr 14, 2015

### cptstubing

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.

4. Apr 14, 2015

### SteamKing

Staff Emeritus
What's the perimeter of a rectangle?

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

5. Apr 15, 2015

### cptstubing

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.

6. Apr 15, 2015

### SteamKing

Staff Emeritus
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?

7. Apr 15, 2015

### cptstubing

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

8. Apr 15, 2015

### Ray Vickson

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?

9. Apr 15, 2015

### cptstubing

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

10. Apr 15, 2015

### Staff: Mentor

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.

11. Apr 15, 2015

### cptstubing

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?

12. Apr 15, 2015

### Staff: Mentor

That's a good start.

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.

13. Apr 15, 2015

### SammyS

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

14. Apr 15, 2015

### Ray Vickson

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?