I have an objective function that has the form:
\begin{equation} \min \qquad \sum_{i} \omega_{i}x_{i}q_{i} \end{equation}
Where $\omega_{i}$ is the weight of variable $i$, $x$ is the decision variable which represents a value between 0 and 1. Finally, $q_{i}$ is the maximum available quantity of item $i$ . There are constraints to the problem, however I won't include them here as I don't think they are necessary. When I solved this problem using a solver in JULIA I found that the result was the same whether or not $q$ was included in the objective function and was wondering how I could interpret it. I can provide further context to the problem if required.
Assuming q is given, try solving Max obj = $x+y$ and obj2 = $3x+ 5y$ where $0 \le x,y \le 9$: All arbitrary.
Other than the optimal value, the solution will be the same. Reason is coefficients (here q) impact the objective value but feasible region/convex hull remains unchanged if constraints are the same.