$Title  A Transportation Problem (TRNSPORT,SEQ=1)
$Ontext


$Offtext


  Set
       i  products for sale   / A,B, Product1, Product1LowCost, Product1SuperLowCost,
                              Product1Purchased, Product2, Product2Purchased /
       mass mass of transitional and output products /Product1MakedFromA, Product1MakedFromB, Product1MakedByConverter,
               Product2ForConverting,  Product2MakedByConverter, Product2MakedFromA, Product2MakedFromB/;
Parameter

       a(i)  cost products in rubles
         / A   -3.25
           B  -3.40
           Product1   5.50
           Product1LowCost 5.20
           Product1SuperLowCost   5.00
           Product1Purchased   -5.75
           Product2   3.80
           Product2Purchased   -4.00
         /;


  Scalar mainProcessCost /-0.35/;
  Scalar filteringProduct1Cost /-0.10/;
  Scalar convertingCost /-0.25/;



  Variables
       z       total  costs in rubles ;

  Positive Variables
                      massForSale(i) of products in tonns
                      massForChemistry(mass);

  Equations
       cost        define objective function
       stageA1
       stageA2
       stageB1
       stageB2
       converter1
       converter2
       converterPerfomance
       product1OkPrice
       product1LowPrice
       product1Contract
       massA
       massB
       factoryPerfomance
       product1MassEquals
       product2MassEquals
       productsConverting;

       cost.. z  =e=  sum(i, a(i)*massForSale(i)) + (massForSale("A") + massForSale("B"))*mainProcessCost
                             + (massForChemistry("Product1MakedFromA")+ massForChemistry("Product1MakedFromB") )*filteringProduct1Cost
                             + massForChemistry("Product2ForConverting")*convertingCost;

       stageA1..  0.15*massForSale("A") =e= massForChemistry("Product1MakedFromA");
       stageA2..  0.85*massForSale("A") =e= massForChemistry("Product2MakedFromA");
       stageB1..  0.25*massForSale("B") =e= massForChemistry("Product1MakedFromB");
       stageB2..  0.75*massForSale("B") =e= massForChemistry("Product2MakedFromB");

       converter1.. 0.5*massForChemistry("Product2ForConverting") =e= massForChemistry("Product1MakedByConverter");
       converter2.. 0.5*massForChemistry("Product2ForConverting") =e=  massForChemistry("Product2MakedByConverter");
       converterPerfomance..  massForChemistry("Product2ForConverting") =l= 50*1000;
       productsConverting..  massForChemistry("Product2ForConverting") =l= massForChemistry("Product2MakedFromB")
                                                                             + massForChemistry("Product2MakedFromA") + massForSale("Product2Purchased");
       product1OkPrice.. massForSale("Product1") =l= 45*1000;
       product1LowPrice.. massForSale("Product1LowCost") =l= 4*1000;
       product1MassEquals.. massForChemistry("Product1MakedFromA")+ massForChemistry("Product1MakedFromB")
                                    + massForChemistry("Product1MakedByConverter") =e=
                                                 massForSale("Product1")+ massForSale("Product1LowCost")
                                                                        + massForSale("Product1SuperLowCost");
       product2MassEquals..   massForChemistry("Product2MakedFromA")+ massForChemistry("Product2MakedFromB")
                                    + massForChemistry("Product2MakedByConverter") =e=  massForSale("Product2");

       product1Contract.. massForSale("Product1")+ massForSale("Product1LowCost")
                                     + massForSale("Product1SuperLowCost") +  massForSale("Product1Purchased") =g= 40*1000;
       massA..  massForSale("A") =l= 100*1000;
       massB.. massForSale("B") =l= 30*1000;
       factoryPerfomance.. massForSale("A")+massForSale("B") =l=100*1000;

  Model transport /all/ ;

  Solve transport using lp maximizing z ;

  Display z.up ;
 Display  'first a set', i, 'then parameter',a ,
  'then the activity level of a variable', massForSale.l, ' and ', massForChemistry.l, mass;