An industrial group manufactures and sells general application fertilizers. The group has three floors in different locations that produce the fertilizer and send it for sale to four warehouses located in different parts. Since the plants are of different age, the Production costs vary according to the modernity of the process used to manufacture the fertilizer. The warehouses work independently, so the price sales per ton differs between them. The costs of transportation from the plants to the warehouses, the cost of production, the capacities of the plants and the demand from the warehouses are presented in the following table:

(Costo transporte = Transportation costs)

Model the problem for the industry group to define the linear programming model to achieve maximize total profits by determining the monthly tons to be shipped from every plant to every warehouse.

Plant Store 1 Costo transporte Store 2 Store 3 Store 4 230 180 210 Production capacity 650 Production Cost 380 300 1 250 2 210 240 180 600 230 270 3 180 210 230 600 350 300 450 600 Maximum demand sale price 500 640 665 670 635 Plant Store 1 Costo transporte Store 2 Store 3 Store 4 230 180 210 Production capacity 650 Production Cost 380 300 1 250 2 210 240 180 600 230 270 3 180 210 230 600 350 300 450 600 Maximum demand sale price 500 640 665 670 635