$\operatorname{maximize} \sum_{i=1}^{50} x_{i}$ subject to $\sum_{i=1}^{50} i \times x_{i} \leq 1000$ $$ \begin{array}{r} x_{i} \leq i^{2}+10, i=1, \ldots, 50 x_{i} \geq 0, i=1, \ldots, 50 \end{array} $$ CS. JG. 126