In order to develop a linear programming model to simulate the activity level which optimizes irrigation, this paper uses data of the farm "Lagoa do Fogão", owned by the Sakai family, in the Guaíra (SP) county, of which 207 ha are irrigated by three center-pivot systems. The objective functions consisted in maximizing the net income of the farm. Winter crops usually cultivated under irrigation in this farm are: industrial tomatoes, wheat, potatoes, peas and beans. The restrictions to the objective function were area, water and markets. The following was concluded: (a) In the area under center-pivot 1, tomatoes (33 ha) and beans (61 ha) should be cultivated; under center-pivot 2, beans (64 ha), and under center-pivot 3 there should be no cultivation with irrigation due to lack of water, (b) To increase the irrigated area under center-pivot 1 beyond the 94 ha until 100 ha, a maximum of US$ 1,815.20 for each extra hectare, may be paid, (c) In the area under center-pivot 2, it was possible to grow 64 ha of beans, using all the available water, that is 125 dm.ha. For the use of higher water amount, the maximum expenditure may come up to US$ 921.42 for each extra 1000 m³ used.
linear programming; water allocation; center-pivot