set CARGOES;

set COMPARTMENTS;

param weight_capacity{COMPARTMENTS};

param space_capacity{COMPARTMENTS};

param weight{CARGOES};

param volume{CARGOES};

param profit{CARGOES};


var x{i in CARGOES, j in COMPARTMENTS} >=0;
# tons of cargo i in compartment j

var y >=0, <=1;
# weight proportion for compartments


maximize total_profit: sum{i in CARGOES, j in COMPARTMENTS} profit[i] * x[i,j];

subject to Cargo_constraints{i in CARGOES}:
sum{j in COMPARTMENTS} x[i,j] <= weight[i];

subject to Space_capacity_constraints{j in COMPARTMENTS}:
sum{i in CARGOES} volume[i] * x[i,j] <= space_capacity[j];

subject to Weight_proportion_constraints{j in COMPARTMENTS}:
sum{i in CARGOES} x[i,j] = weight_capacity[j] * y;


data;

set CARGOES:= 1 2 3 4;

set COMPARTMENTS:= front center back;

param:	weight_capacity	space_capacity :=
 front	12	7000
 center	18	9000
 back	10	5000 ;	

param:	weight volume profit :=
 1	20	500	320
 2	16	700	400
 3	25	600	360 
 4	13	400	290;