Continous Integer Knapsack Set

KI={(s,y)R+1×Z+n:j=1najyjb+s}K^{I}=\left\{(s, y) \in \mathbb{R}_{+}^{1} \times \mathbb{Z}_{+}^{n}: \sum_{j=1}^{n} a_{j} y_{j} \leq b+s\right\}

Mixed Integer Rounding Ungleichung