Hello

I do not know how to solve the following problem. Operations Research is not my specialty.
Who could help me?

The problem is the following:

I have the the following objective function $\displaystyle 3x + 2y + 5z$

Subject to:

$\displaystyle
x + 2y + z \leq{430}
$
$\displaystyle
3x + 2z \leq{460}
$
$\displaystyle
x + 4y \leq{420}
$

If I change the objective function and I propose the following one: $\displaystyle 6x + 4y + z$.
Does this function still get an optimal profit? I need to justify this by doing a sensitivity analysis.

Thanks