Economics

In a poultry production area there are some producers of balanced feed (producers) and small poultry farms that require this feed for their birds (customers). Consider the problem of weekly production and distribution of feed to farms. Assume that the set of feed producing units is given by the set P = {p1, p2, ..., p8}, and the set of poultry farms is identified by the set C= {m1, m2, ..., m12}. The following data is available:

The estimated weekly demand of the farms (tonnes), The maximum weekly production capacity of each balancing producer (tons), The distances (in Km) between each plant and the destinations, The unit costs of production per plant ($/ton), The estimated unit shipping cost of 8 cents./unit/km, The unit sale price in each PVP zone ($/ton) We want to determine how the feed should be distributed to the farms to maximize the total income of the balanced producers (sales - total cost of production and shipping).

Model the problem, that is, identify:

Indexes Data (use vector and matrix notation for data) Decision variables Objective Function restrictions