# SETS

set I;
param n;
set J := 1..n;

# PARAMS

param b{J}; #Work days
param d{I,J}; #Max demand
param r{I};   #Revenues
param c{I};   #Cost
param q{I};   #Max production
param f{I};   
param l{I};
param m{I};   #Inventory cost
param K;

# VARIABLES

var X{I,J} #Prod
var V{I,J} #Sold
var Z{I,J} #Store

# OBJECTIVE FUNCTION

mazimize Profit:
	sum{i in I,j in J} V[i]*r[i]-(c[i]X[i,j] + m[i]*Z[i,j])
	
# CONSTRAINTS

subject to MaxProdConstraint {j in J}:
	sum {i in I} Z[i,j] <= K

subject to MaxSellConstraint {i in I, j in J}:
	V[i,j] <= d[i,j]

subject to InventoryConstraint {i in I, j in J}:
	Z[i,j]-Z[i,j-1]+X[i,j]-V[i,j]

subject to InitialProduction {i in I}:
	X[i,0] = 0

subject to ConstantProduction {j in J}:
	sum{i in I} x[i][j] {x[i][j]}/{q[i]} <= b[j]