This Bachelor thesis examines two possible approaches to solve optimal
control problems. Therefore, a biological problem with an economic
application will be introduced and solved by Pontryagin’s maximum
principle on the one hand and using Green’s theorem on the other hand.
The considered problem concerns fish farming. Due to economic sciences it
is about maximizing profit. This is realized by an optimal fish farming
schedule. To determine the optimal schedule a mathematical model is needed.
Thus, the problem belongs to Operations Research. Both approaches will be
explained step by step and the necessary definitions and theorems will be
provided. In the end the aim is to specify one/the optimal solution.
Several papers and thesis by different authors form the basis of this
Bachelor thesis. The task is to retrace their approaches. Therefore, it is
necessary to perform auxiliary calculations. The main focus is on
mathematical correctness. Furthermore, totally own approaches will be made
at given point.