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The production of coffee like all other culture requires resources in labor and in inputs of which the quantities that the producer can arrange are limited. The question to know : how to combine these resources in complex, concurrencies and moving environment, in order to reach a good level of production to the possible lowest cost, to put himself the most often in economic analysis. Thus, in order to contribute to bring an answer to this question by the determination of the optimal quantities of the production factors, the present study based its analysis on a linear programming model integrating socio-economic characteristic and the description of the techniques of coffee production during the period of useful life of the coffee plantation. This linear programming model based on the principle that the agricultural operator seeks to minimize its cost of production considering its level of production while satisfying a set of constraints.

Depending on the results of this model, farm practice is far from theoretical optimum in the sense of allocation of production factors. For the weeding, main maintenance activity in caféiculture, the theoretical optimization of factor work would correspond at the following doorsteps :

3 weddings on plantations of 4 at 7 years,
2 weddings on plantations of 8 at 19 years,
1 weeding on plantations of 20 at 25 years.

The optimal value of the production cost rises to 5 416 570 FCFAS / ha for the 25 years of useful life of the plantation. That is 405. 74 FCFA as cost of production of one kilogram of coffee merchant for a level of middle production of 600 kg / ha. The analysis of the profitability shows that this profitability is bound as well to the output that to the price of purchase of the product. The culture of coffee is not really profitable and becomes only competitive if it allows the producer to clear a raw margin superior or equal in 259 160 FCFA on a plantation of one hectare. It is also evident from our analyses that factor work occupies more 60% in the system of production. The system marks production of the coffee of the zone can be characterized as intensive system in work.

Key words : profitability, linear programming, labour, coffee, Akébou, Togo

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