Date of Award


Degree Type


Degree Name

Bachelor of Science (Mathematics) Honours


Faculty of Science. Technology and Engineering

First Advisor

Dr Steven Schilizzi

Second Advisor

Mr Gavin White


In this thesis we consider the following problem: Suppose that a farmer wishes to determine the best course of action to maximise returns from his I her land which has undergone some form of degradation. In order to rehabilitate the land, the farmer may have to change to a different farming practice for some time until the previous practice becomes profitable again. Switching from cropping to rehabilitation Of from rehabilitation to cropping incurs costs. From an economical point of view, the question then arises: When is the optimal time to switch from cropping· to rehabilitation and when is it optimal to switch back to cropping again in order to maximise profit? In tills thesis, we give a mathematical formulation of the farmer's problem and derive necessary conditions for optimality using the calculus of variations. We then apply our model to the specific case of a rotation between wheat farming and oil mallee plantation. We determine optimal switching times for two scenarios - break even and current performance levels- and explore the effects of the rates of change of the water level and the discount rate on the optimal switching times.

Included in

Mathematics Commons