SETs

i indexes of plants /seattle, san-diego/
j indexes of markets /new-york, chicago, topeka/   ;

PARAMETERS
a(i)   capacity of plant i
/    seattle    350
     san-diego  600
/

b(j)   demand of market j
/    new-york 325
     chicago  300
     topeka   275
/
;

Table d(i,j)  distance in thousands of miles
             new-york       chicago       topeka
seattle      2.5            1.7           1.8
san-diego    2.5            1.8           1.4 ;


Scalar f frieght in dollars per cases per thousand miles /90/;

parameters c(i,j)  transportation costs in thousands of dollars per case ;
c(i,j)= f*d(i,j)/1000;

Variables

x(i,j)   shipment quantities in cases
Z        total transportation costs in thousands of dollars ;

positive variable x ;

Equations


cost        define objective function

supply(i)   supply limit at plant i

demand(j)   satisfy demand at market j   ;


cost..           z=e= sum((i,j),c(i,j)*x(i,j));
supply(i)..      sum(j,x(i,j))=l=a(i);
demand(j)..      sum(i,x(i,j))=g=b(j);


Model TP /all/

solve TP using lp minimizing z ;

Display  x.l , z.l ;



