Optimization Algorithms

[Kartit]

Hi,
I am new to machine learning, and I am experimenting with neural nets.
I would like to know if the they are suitable for my problem and I am
lost between linear programming/genetic algorithms and neural nets. I
am trying to optimize the number of doctors to allocate in order to
minimize patients non treated in case of an emergency.

my data sets format as follows:
1. Event / Patients treated / patients non treated
2. Event / Doctor / speciality.
3. Event / number of doctors involved in best case / worst case
scenario

my constraints are: number of patients non treated should not exceed a
parameter X.
Output: How much doctors to allocate from each speciality.

I hope this explains my problem, I am just asking for a good approach
if this should use linear programming the finding an optimal solution
using genetic algorithms? any suggestions I would appreciate it.