Sets

i Regions /A, B, C, D, E, F, G/

j Customers /A, B, C, D, E, F, G/;

Parameters

c(i, j) Unit shipping costs between regions

/A.A 0, A.B 7, A.C 4, A.D 5, A.E 12, A.F 7, A.G 14

B.A 7, B.B 0, B.C 11, B.D 12, B.E 12, B.F 14, B.G 11

C.A 4, C.B 11, C.C 0, C.D 7, C.E 16, C.F 3, C.G 11

D.A 5, D.B 12, D.C 7, D.D 0, D.E 15, D.F 5, D.G 9

E.A 12, E.B 12, E.C 16, E.D 15, E.E 0, E.F 14, E.G 6

F.A 7, F.B 14, F.C 3, F.D 5, F.E 14, F.F 0, F.G 8

G.A 14, G.B 11, G.C 11, G.D 9, G.E 6, G.F 8, G.G 0/

demand(i) Demand in tons

/A 100, B 200, C 120, D 45, E 250, F 80, G 75/

capacity(i) Facility capacity in tons

/A 225, B 500, C 300, D 900, E 600, F 130, G 110/

fixed_cost(i) Fixed cost of opening a facility

/A 1000, B 1500, C 1200, D 2500, E 1800, F 800, G 750/;

Variables

x(i) Facility open decision (binary)

y(i, j) Flow from facility i to customer j;

Binary Variables

x(i) Facility open decision;

Positive Variables

y(i, j) Flow from facility i to customer j;

Equations

obj Objective function

supply(i) Supply constraint at each facility

demand(j) Demand constraint at each customer; //here

obj.. z =e= sum(i, fixed_cost(i) * x(i)) + sum((i, j), c(i, j) * y(i, j)); //here

supply(i).. sum(j, y(i, j)) =l= capacity(i) * x(i);

demand(j).. sum(i, y(i, j)) =g= demand(j); //here

* Facility open decision

x('B') = 1; //here

x('C') = 1; //here

x('F') = 1; //here

Model facility_location_option1 /all/;

Option optcr = 0.0;

Solve facility_location_option1 using mip minimizing z; //here

Display x.l, y.l;

The new facilities are opened in region B, C, and F. Develop a distribution plan that minimizes total shipping and fixed costs while satisfying demands at the regions (Use GAMS to develop the models). Please fix those errors which has //here sign at the end of the lines.