# Problem formulation

Pywr attempts to solve the supply demand balance each timestep by framing the problem as a linear programme.

\begin{split}\begin{align} & \text{maximize} && \mathbf{c}^\mathrm{T} \mathbf{x}\\ & \text{subject to} && A \mathbf{x} \leq \mathbf{b} \\ & \text{and} && \mathbf{x} \ge \mathbf{0} \end{align}\end{split}