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 3x + 2y + 5z

Subject to:

 <br />
x + 2y + z \leq{430}<br />
 <br />
3x + 2z \leq{460}<br />
 <br />
x + 4y \leq{420}<br />

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