Operations Research - sensitivity analysis problem

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