Bounding Region Inequalities for Solid Rectangular Box in First Octant

[Winzer]

Homework Statement

Ok I just wanted to make sure of this one.
Write inequalities to describe the region:
The solid rectangular box in the first octant bounded by the pane x=1 y=2 z=3.

The Attempt at a Solution

I thought of it as the volume of the box bounded boy the planes so:
$$0\leq xyz\leq 6$$

 

[Hurkyl]

So, you are claiming that the point

(1000, -1/100, -1/10)​

lies in the box?

 

[Winzer]

ok so how about

$$0\leq x+y+z \leq 6$$

 

[Hurkyl]

What about the point (100, 200, -300)?

(Oh, and why do you think (1000, -1/100, -1/10) isn't in the box?)

 

[Winzer]

What about the point (100, 200, -300)?

(Oh, and why do you think (1000, -1/100, -1/10) isn't in the box?)

They are all in the box. Should I just make a contraint for each varible?

 

[Hurkyl]

Should I just make a contraint for each varible?

That's certainly a reasonable thing to do.