I need help transforming this Mathematical Programming model into a solvable model
$ \min \delta$
$\frac{190(E_j-\sum_ix_{ij})}{P_j-\sum_iQ_ix_{ij}}\leq\delta \ \ \ \ \forall j$
$\sum_j x_{ij} \leq S_i \ \ \ \ \forall i$
$ P_j-\sum_iQ_ix_{ij}\geq0.4P_j\ \ \ \ \forall j$
$ \sum_ix_{ij}\geq0\ \ \ \ \forall j$
$x_{ij}$ is a continuous variable, all the rest are parameters
I tried fractional programming transformation but I can't get it right. Thanks in advance. Any help will be much appreciated!
One approach to solve this problem is to perform a bisection search on $\delta$. For each fixed $\delta$, you can clear the denominator on the corresponding constraint to linearize. If the resulting LP problem is infeasible, change the lower bound of the search interval to $\delta$. If the resulting LP problem is feasible, change the upper bound of the search interval to $\delta$. Repeat until the difference in bounds is sufficiently small.