Length : around 15 minutes
Run the labour2.gms model and save it under the name travail3.gms. You can now modify the model and loosen all the constraints.
« A given farm can grow three types of crop, wheat, maize and tomato, and use two crop practices, extensive and intensive. The area to be cultivated must be determined for each production-technology combination, knowing that :
The objective of the farmer is maximize his income.
Water needs are as follows :
| Water needs (thousands of m3) | ||
| Technology | extensive | intensive |
| Wheat | 0 | 2 |
| Maize | 4 | 6 |
| Tomato | 3 | 5 |
Labour needs are as follows :
| Labour needs (h/ha) | |||
| Technology | Period | ||
| Winter | Summer | ||
| Wheat | extensive | 10 | 5 |
| intensive | 15 | 10 | |
| Maize | extensive | 10 | 35 |
| Intensive | 10 | 40 | |
| Tomato | extensive | 10 | 70 |
| Intensive | 10 | 90 | |
Yields and costs are as follows :
| Yield (ton/ha) | Cost (€/ha) | |||
| Technology | extensive | intensive | extensive | Intensive |
| Wheat | 4.5 | 5.0 | 250 | 300 |
| Maize | 8.0 | 10.0 | 400 | 500 |
| Tomato | 13.0 | 16.0 | 1200 | 1350 |
The selling price of wheat is 150€/ton, that of maize 150€/ton, and that of tomato 185€/ton.
The farm area is 50 ha, and the farmer can work 1000 hours in summer and 1000 hours in winter, and has 150 thousand m3 for irrigation. »
The farmer now has the possibility of hiring workers at 10€ an hour, of buying water at 50€ per m3 and of renting land at 150€/ha. »
What cropping pattern was chosen, and what is the optimum income for the farmer ?
Then check the solution : 
