param n;
param T;
param Smax;
param Smin;
param Si;
param Sf;
param Amax;

param Q{1..12};
param B{1..4};
param d{1..4,1..12};

var x{1..n};
var R{1..T};
var D{1..T};
var S{0..T};

maximize f: sum{i in 1..n} B[i]*x[i];
s.t. c_1{t in 1..T} : S[t] >= Smin;
s.t. c_2{t in 1..T} : S[t] <= Smax;
s.t. c_3{i in 1..n} : x[i] >= 0;
s.t. c_4 : sum{i in 1..n} x[i] <= Amax;
s.t. c_5{t in 1..T} : sum{i in 1..n} d[i,t]*x[i]= 0.5*D[t];
s.t. c_6 : S[0]= Si;
s.t. c_7{t in 1..T} : S[t]= S[t-1] + Q[t] - R[t];
s.t. c_8{t in 1..T} : D[t] <= R[t];
s.t. c_9 : S[T] >= Sf;