Transportation problem (Minimal Cost)

There are three sellers in different cities: CityA, CityB and CityC.
They have 250, 130 and 250 tons of goods. 

There are four buyers in CityD, CityE, CityF and CityG.
They ordered 75, 230, 240 and 70 tons of goods for their production.

The following costs of transportation for one ton of goods apply from one city 
to another city:
from\to  (D) (E) (F) (G)
CityA (A) 10  20  15  20
CityB (B) 20  15   5  10
CityC (C) 10  15   5  15

The stocks in city A are denoted with x_A
The requests for city D are denoted with x_D
The cost of transportation from one city to another is denoted by C_from_to,
for example cost from CityC to CityF is C_C_F.

## parameters
x_A  = 250
x_B  = 130
x_C  = 250

x_D  = 75
x_E  = 230
x_F  = 240
x_G  = 70

c_A_D = 10
c_A_E = 20
c_A_F = 15
c_A_G = 20
c_B_D = 20
c_B_E = 15
c_B_F = 5
c_B_G = 10
c_C_D = 10
c_C_E = 15
c_C_F = 5
c_C_G = 15
## end parameters

The decision variables are tons transported from one city to another.
They are denoted as x_from_to:
X_A_D = tons from CityA to CityD, etc.

## DECISION
x_A_D
x_A_E
x_A_F
x_A_G
x_B_D
x_B_E
x_B_F
x_B_G
x_C_D
x_C_E
x_C_F
x_C_G
## END DECISION

All orders should be performed while the transportation costs should be minimized.

## COST
x_A_D * c_A_D + x_A_E * c_A_E + x_A_F * c_A_F + x_A_G * c_A_G  + &
x_B_D * c_B_D + x_B_E * c_B_E + x_B_F * c_B_F + x_B_G * c_B_G  + &
x_C_D * c_C_D + x_C_E * c_C_E + x_C_F * c_C_F + x_C_G * c_C_G  
## END COST


The constraints are defined in terms of the transported amount from one 
seller or to one buyer.

For example:
Amount transported from CityA cannot be more than 250 tons:
X_A_D + X_A_E + X_A_F + X_A_G <= 250

## Constraint
x_A_D + x_A_E + x_A_F + x_A_G < x_A
x_B_D + x_B_E + x_B_F + x_B_G < x_B
x_C_D + x_C_E + x_C_F + x_C_G < x_C
## END constraint

## EQUALITIES
x_A_D + x_B_D + x_C_D         =x_D
x_C_E + x_B_E + x_A_E         =x_E
x_A_F + x_B_F + x_C_F         =x_F
x_A_G + x_B_G + x_C_G         =x_G
## END EQUALITIES

