set NUTR ordered;
set FOOD ordered;

param cost {FOOD} >= 0;
param f_min {FOOD} >= 0, default 0;
param f_max {j in FOOD} >= f_min[j], default Infinity;

param n_min {NUTR} >= 0, default 0;
param n_max {i in NUTR} >= n_min[i], default Infinity;

param amt {NUTR,FOOD} >= 0;

# --------------------------------------------------------

var Buy {j in FOOD} integer >= f_min[j], <= f_max[j];

# --------------------------------------------------------

minimize Total_Cost:  sum {j in FOOD} cost[j] * Buy[j];

minimize Nutr_Amt {i in NUTR}: sum {j in FOOD} amt[i,j] * Buy[j];

# --------------------------------------------------------

subject to Diet {i in NUTR}:
   n_min[i] <= sum {j in FOOD} amt[i,j] * Buy[j] <= n_max[i];