# Is that Ok to exclude fixed components from an objective function?

Suppose we have the following objective function with one decision variable $$x_i$$ where $$p_i$$ is a fixed parameter for each $$i$$ and also, $$a$$ is a constant for the problem
\begin{align} \label{eq} \max \sum^N_{i=1} p_i(a+1-x_i) = \max \bigg{(}\sum^N_{i=1} p_ia +\sum^N_{i=1}p_i -\sum^N_{i=1} p_i x_i\bigg{)} \end{align}

As the first two components: $$\sum^N_{i=1} p_ia$$ and $$\sum^N_{i=1}p_i$$ are fixed and changing $$x_i$$ won't affect them anyway. Is there any difference if I excluded the fixed components from the objective function and set the objective function to be $$$$\max \sum^N_{i=1} -p_ix_i = \min \sum^N_{i=1} p_ix_i?$$$$

Of course, the objective function value is not the same before and after excluding the fixed components, but will the values of $$x_i$$ be the same in both cases?