I am currently preparing for my finals and I came across one problem which I couldn't solve. I've been struggling with this for a few days.
The farmer owns $50$ animals and land that can feed $1000$ animals. The natural increase for a small number of animals is at the annual level of $p = 1$. To provide incentives, the state offers a free lease of land in the same area for a period of $5$ years. At which point in time should the farmer start using additional land to:
- Have the largest number of animals after $10$ years?
- Have the highest average number of animals in $10$ years?
The use of numerical methods is allowed.
I am familiar with logistic growth (Verhulst's model), but I don't know how to start. Any help would be much appreciated. Sorry if my English was bad.