Alternative Equation Formats

$$\begin{array}{rl}(\underset{i=1}{\overset{I_k}{\sum <!--\; \sum \; -->}}{c}_i\ge <!--\; \ge \; -->\underset{i=1}{\overset{I_{k-<!--\; -\; -->1}}{\sum <!--\; \sum \; -->}}{c}_i+bc& \mathrm{o}\mathrm{r}\underset{i=1}{\overset{I_k}{\sum <!--\; \sum \; -->}}{c}_i\ge <!--\; \ge \; -->\frac{n}{\mathsf{\text{numbin}}}\ast <!--\; \ast \; -->k)\\ \mathrm{a}\mathrm{n}\mathrm{d}& \underset{i=1}{\overset{I_k}{\sum <!--\; \sum \; -->}}{c}_i>\underset{i=1}{\overset{I_{k-<!--\; -\; -->1}}{\sum <!--\; \sum \; -->}}{c}_i\\ \mathrm{a}\mathrm{n}\mathrm{d}& \underset{i=1}{\overset{I_k}{\sum <!--\; \sum \; -->}}{c}_i<n\end{array}$$

$$\begin{array}{rl}(\underset{i=1}{\overset{I_k}{\sum <!--\; \sum \; -->}}{c}_i\ge <!--\; \ge \; -->\underset{i=1}{\overset{I_{k-<!--\; -\; -->1}}{\sum <!--\; \sum \; -->}}{c}_i+bc& \mathrm{o}\mathrm{r}\underset{i=1}{\overset{I_k}{\sum <!--\; \sum \; -->}}{c}_i\ge <!--\; \ge \; -->\frac{n}{\mathsf{\text{numbin}}}\ast <!--\; \ast \; -->k)\\ \mathrm{a}\mathrm{n}\mathrm{d}& \underset{i=1}{\overset{I_k}{\sum <!--\; \sum \; -->}}{c}_i>\underset{i=1}{\overset{I_{k-<!--\; -\; -->1}}{\sum <!--\; \sum \; -->}}{c}_i\\ \mathrm{a}\mathrm{n}\mathrm{d}& \underset{i=1}{\overset{I_k}{\sum <!--\; \sum \; -->}}{c}_i<n\end{array}$$

\begin{align*} \bigg(\sum _{i=1}^{I_ k}{c_ i} \geq \sum _{i=1}^{I_{k-1}}{c_ i} + bc & \quad \mathrm{or} \quad \sum _{i=1}^{I_ k}c_ i \geq \frac{n}{\Argument{numbin}}*k\bigg)\\ \mathrm{and} & \quad \sum _{i=1}^{I_ k}{c_ i} > \sum _{i=1}^{I_{k-1}}{c_ i} \\ \mathrm{and} & \quad \sum _{i=1}^{I_ k}{c_ i} < n \end{align*}