Optimizing resources with Linear Programming

Location problem

A company has the exclusive for distribution of a product in 4 populations. Potential demand has been determined in a market research, according to he shows up in the following board:

Population 1 Population 2 Population 3 Population 4
3000 units 2000 units 2500 units 2700 units

Is knwon that the transport expenses are 0.02€ per Km and unit transported. The distance among towns is the shows in the board following:

  Population 1 Population 2 Population 3 Population 4
Population 1 - 25Km 35Km 40Km
Population 2 25Km - 20Km 40Km
Population 3 35Km 20Km - 30Km
Population 4 40Km 40Km 30Km -

In order to cheap the transportation costs is decided to install in two of that 4 populations a store with capability for 6000 units. Determining in wich populations must install the stores.


Determining decision variables and expressing them algebraically. In this case:

Determining the restrictions and expressing them as equations or inequalities in function of the decision variables.

Expressing all implicit conditions established by the origin of variables: negativeness, integer, only a few allowed values... . In this case, the restrictions are that the delivered units from each store can't be negatives and also the variable determine that determine if a store is created or not must be boolean (0 isn't created, 1 yes):

Determining objective function:


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