$LOU_{min} = \underset{(m_1,\dots,m_n)\in\mathbb{R}^n}{\text{min}} \sum_{i=1}^N - u_i\left(m_i\right)$
$ 0.1 \leq m_i - b_i < p_i \qquad \forall i \in \{1,\dots,n\}$
$p_i - m_i \leq rmax_i \qquad \forall i \in \{1,\dots,n\}$
$Q_{req} = \sum_{i=1}^N \left(p_i - m_i\right)$
$u_i(m_i) = {m_i}^{0.5}$ and in other cases ${m_i}^{0.4}$