Solving f(x,y,z) with x,y,z Constraints

[DrunkApple]

Homework Statement

f(x,y,z) = e^(2x-z)
W: x+y+z ≤ 1, x,y,z ≥ 0

Homework Equations

0 ≤ x ≤ 1-y-z
0 ≤ y ≤ 1-x-z
0 ≤ z ≤ 1-x-y

The Attempt at a Solution

I tried dzdydx and dydzdx but they don't work...
or am I doing something wrong?

 

[jambaugh]

You will note that the boundaries are symmetric under permutations of x, y, and z. Thus w.r.t. the boundary order of integration shouldn't matter.

The integrand will be quite easy to integrate. I suggest you factor it into e^(2x) e^(-z).

You just have to set up your boundaries of integration correctly. Can you show us some of your attempts?

 

[DrunkApple]

Isn't that the correct boundaries that I set up in relevant equations?
or is that wrong?
I would love to post my work... but it's so much mess right now... it's like everywhere... If I can get the right boundaries I feel like I can get it right

 

[jambaugh]

Give me what you got...

integral from what to what, from what to what, from what to what of what dwhatdwhatdwhat?