- #1
twoflower
- 368
- 0
Hi,
I want to find global extremes of function
[tex]
f(x,y,z) = xy^{2}y^3
[/tex]
on the set
[tex]
M = \left\{[x,y,z] \in \mathbb{R}^{3}, x+2y+4z = a, x,y,z > 0\right\}
[/tex]
I need to show that this is compact. Because I'm in [itex]\mathbb{R}^{n}[/itex] it is sufficient to show it is closed and bounded. Closeness (is this the right noun?) is obvious. How to show it is bounded as well? Is it trivial, ie. may I just say that it is some bounded plane or how?
Thank you.
I want to find global extremes of function
[tex]
f(x,y,z) = xy^{2}y^3
[/tex]
on the set
[tex]
M = \left\{[x,y,z] \in \mathbb{R}^{3}, x+2y+4z = a, x,y,z > 0\right\}
[/tex]
I need to show that this is compact. Because I'm in [itex]\mathbb{R}^{n}[/itex] it is sufficient to show it is closed and bounded. Closeness (is this the right noun?) is obvious. How to show it is bounded as well? Is it trivial, ie. may I just say that it is some bounded plane or how?
Thank you.
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