Length : around 40 minutes
Write the following model.
An arable crop farmer growing special crops in the Centre-Val de Loire region (data INOSYS Système GC 131 ) has 110 ha of land. Irrigation and the economic environment of his farm offers him a large range of production options : soft wheat, durum wheat, spring barley, potatoes for human consumption, sugar beets and rapeseed. Five of these crop types are irrigated in order to ensure high quality regular production. The farmer has 60 000 m3 of water.
Irrigation needs and economic data are shown in the table below :
Irrigation
| Crops | Volume in m3/ha | |||
| Soft wheat | 175 | |||
| Durum wheat | 350 | |||
| Spring barley | 700 | |||
| Potato for human consumption | 1800 | |||
| sugar beet | 1750 | |||
Technico-economic data
| Crops | Yields (qx/ha) | Prices/qx (€) | Total costs (€/ha) | |
| Soft wheat | 85 | 16 | 460 | |
| Durum wheat | 71 | 28 | 565 | |
| Spring barley | 70 | 17.5 | 470 | |
| Potato for human consumption | 495 | 14 | 4210 | |
| sugar beet | 950 | 2.6 | 1082 | |
| Rapeseed | 40 | 38 | 490 | |
Source : from the Système GC 131 of the INOSYS network of agricultural chambers in the Centre Val de Loire region. 2016.
For agronomic reasons,
– Oilseed crops cannot be grown more than once every three years on the same plot,
– cereal crops cannot be grown two years in a row on the same plot,
– and sugar beets or potatoes can only be cultivated once every six years.
What is the optimum cropping pattern for this farmer ? What is his optimum income ?
Then check the solution: 
