```json
{
  "sym_variables": [
    ("x0", "milligrams of vitamin B9"),
    ("x1", "milligrams of vitamin B4"),
    ("x2", "milligrams of vitamin B2"),
    ("x3", "milligrams of vitamin B12"),
    ("x4", "milligrams of vitamin E"),
    ("x5", "milligrams of vitamin A"),
    ("x6", "milligrams of vitamin K"),
    ("x7", "milligrams of vitamin B7")
  ],
  "objective_function": "3.06*x0 + 1.0*x1 + 9.75*x2 + 5.81*x3 + 8.24*x4 + 7.02*x5 + 6.2*x6 + 1.24*x7",
  "constraints": [
    "2*x0 + 4*x1 + 6*x2 + 12*x3 + 4*x4 + 7*x5 + 3*x6 + 9*x7 <= 628",
    "21*x0 + 31*x1 + 28*x2 + 2*x3 + 31*x4 + 15*x5 + 24*x6 + 3*x7 <= 636",
    "2*x0 + 12*x3 >= 50",
    "4*x1 + 3*x6 >= 42",
    "12*x3 + 3*x6 >= 59",
    "4*x1 + 6*x2 >= 61",
    "12*x3 + 4*x4 + 3*x6 >= 43",
    "2*x0 + 12*x3 + 9*x7 >= 43",
    "2*x0 + 6*x2 + 7*x5 >= 43",
    "2*x0 + 4*x1 + 7*x5 >= 43",
    "2*x0 + 6*x2 + 3*x6 >= 43",
    "2*x0 + 4*x1 + 9*x7 >= 43",
    "4*x1 + 12*x3 + 7*x5 >= 43",
    "12*x3 + 7*x5 + 9*x7 >= 43",
    "4*x1 + 6*x2 + 12*x3 >= 43",
    "12*x3 + 4*x4 + 3*x6 >= 75",
    "2*x0 + 12*x3 + 9*x7 >= 75",
    "2*x0 + 6*x2 + 7*x5 >= 75",
    "2*x0 + 4*x1 + 7*x5 >= 75",
    "2*x0 + 6*x2 + 3*x6 >= 75",
    "2*x0 + 4*x1 + 9*x7 >= 75",
    "4*x1 + 12*x3 + 7*x5 >= 75",
    "12*x3 + 7*x5 + 9*x7 >= 75",
    "4*x1 + 6*x2 + 12*x3 >= 75",
    "12*x3 + 4*x4 + 3*x6 >= 72",
    "2*x0 + 12*x3 + 9*x7 >= 72",
    "2*x0 + 6*x2 + 7*x5 >= 72",
    "2*x0 + 4*x1 + 7*x5 >= 72",
    "2*x0 + 6*x2 + 3*x6 >= 72",
    "2*x0 + 4*x1 + 9*x7 >= 72",
    "4*x1 + 12*x3 + 7*x5 >= 72",
    "12*x3 + 7*x5 + 9*x7 >= 72",
    "4*x1 + 6*x2 + 12*x3 >= 72",
    "12*x3 + 4*x4 + 3*x6 >= 69",
    "2*x0 + 12*x3 + 9*x7 >= 69",
    "2*x0 + 6*x2 + 7*x5 >= 69",
    "2*x0 + 4*x1 + 7*x5 >= 69",
    "2*x0 + 6*x2 + 3*x6 >= 69",
    "2*x0 + 4*x1 + 9*x7 >= 69",
    "4*x1 + 12*x3 + 7*x5 >= 69",
    "12*x3 + 7*x5 + 9*x7 >= 69",
    "4*x1 + 6*x2 + 12*x3 >= 69",
    "12*x3 + 4*x4 + 3*x6 >= 74",
    "2*x0 + 12*x3 + 9*x7 >= 74",
    "2*x0 + 6*x2 + 7*x5 >= 74",
    "2*x0 + 4*x1 + 7*x5 >= 74",
    "2*x0 + 6*x2 + 3*x6 >= 74",
    "2*x0 + 4*x1 + 9*x7 >= 74",
    "4*x1 + 12*x3 + 7*x5 >= 74",
    "12*x3 + 7*x5 + 9*x7 >= 74",
    "4*x1 + 6*x2 + 12*x3 >= 74",
    "12*x3 + 4*x4 + 3*x6 >= 54",
    "2*x0 + 12*x3 + 9*x7 >= 54",
    "2*x0 + 6*x2 + 7*x5 >= 54",
    "2*x0 + 4*x1 + 7*x5 >= 54",
    "2*x0 + 6*x2 + 3*x6 >= 54",
    "2*x0 + 4*x1 + 9*x7 >= 54",
    "4*x1 + 12*x3 + 7*x5 >= 54",
    "12*x3 + 7*x5 + 9*x7 >= 54",
    "4*x1 + 6*x2 + 12*x3 >= 54",
    "12*x3 + 4*x4 + 3*x6 >= 40",
    "2*x0 + 12*x3 + 9*x7 >= 40",
    "2*x0 + 6*x2 + 7*x5 >= 40",
    "2*x0 + 4*x1 + 7*x5 >= 40",
    "2*x0 + 6*x2 + 3*x6 >= 40",
    "2*x0 + 4*x1 + 9*x7 >= 40",
    "4*x1 + 12*x3 + 7*x5 >= 40",
    "12*x3 + 7*x5 + 9*x7 >= 40",
    "4*x1 + 6*x2 + 12*x3 >= 40",
    "12*x3 + 4*x4 + 3*x6 >= 48",
    "2*x0 + 12*x3 + 9*x7 >= 48",
    "2*x0 + 6*x2 + 7*x5 >= 48",
    "2*x0 + 4*x1 + 7*x5 >= 48",
    "2*x0 + 6*x2 + 3*x6 >= 48",
    "2*x0 + 4*x1 + 9*x7 >= 48",
    "4*x1 + 12*x3 + 7*x5 >= 48",
    "12*x3 + 7*x5 + 9*x7 >= 48",
    "4*x1 + 6*x2 + 12*x3 >= 48",
    "12*x3 + 4*x4 + 3*x6 >= 78",
    "2*x0 + 12*x3 + 9*x7 >= 78",
    "2*x0 + 6*x2 + 7*x5 >= 78",
    "2*x0 + 4*x1 + 7*x5 >= 78",
    "2*x0 + 6*x2 + 3*x6 >= 78",
    "2*x0 + 4*x1 + 9*x7 >= 78",
    "4*x1 + 12*x3 + 7*x5 >= 78",
    "12*x3 + 7*x5 + 9*x7 >= 78",
    "4*x1 + 6*x2 + 12*x3 >= 78",
    "15*x5 + 24*x6 >= 73",
    "31*x1 + 24*x6 >= 54",
    "21*x0 + 15*x5 >= 71",
    "28*x2 + 24*x6 >= 79",
    "21*x0 + 3*x7 >= 42",
    "31*x1 + 3*x7 >= 31",
    "21*x0 + 24*x6 >= 79",
    "2*x3 + 3*x7 >= 59",
    "2*x3 + 24*x6 >= 77",
    "31*x1 + 15*x5 >= 59",
    "2*x3 + 15*x5 >= 35",
    "15*x5 + 24*x6 + 3*x7 >= 78",
    "21*x0 + 28*x2 + 15*x5 >= 78",
    "31*x1 + 15*x5 + 3*x7 >= 78",
    "15*x5 + 24*x6 + 3*x7 >= 78",
    "28*x2 + 2*x3 + 3*x7 >= 78",
    "31*x1 + 24*x6 + 3*x7 >= 78",
    "31*x1 + 2*x3 + 15*x5 >= 78",
    "21*x0 + 2*x3 + 15*x5 >= 78",
    "31*x1 + 31*x4 + 15*x5 >= 78",
    "31*x1 + 28*x2 + 2*x3 >= 78",
    "28*x2 + 31*x4 + 3*x7 >= 78",
    "31*x1 + 15*x5 + 24*x6 >= 78",
    "31*x1 + 28*x2 + 3*x7 >= 78",
    "21*x0 + 28*x2 + 31*x4 >= 78",
    "28*x2 + 15*x5 + 3*x7 >= 78",
    "2*x3 + 31*x4 + 24*x6 >= 78",
    "28*x2 + 2*x3 + 15*x5 >= 78",
    "2*x3 + 15*x5 + 3*x7 >= 78",
    "31*x1 + 31*x4 + 3*x7 >= 78",
    "21*x0 + 28*x2 + 2*x3 >= 78",
    "28*x2 + 2*x3 + 24*x6 >= 78",
    "21*x0 + 15*x5 + 24*x6 >= 78",
    "2*x3 + 24*x6 + 3*x7 >= 78",
    "31*x4 + 15*x5 + 3*x7 >= 78",
    "21*x0 + 24*x6 + 3*x7 >= 78",
    "31*x1 + 28*x2 + 31*x4 >= 78",
    "21*x0 + 31*x4 + 3*x7 >= 78",
    "31*x1 + 2*x3 + 3*x7 >= 78",
    "28*x2 + 31*x4 + 24*x6 >= 78",
    "31*x4 + 24*x6 + 3*x7 >= 78",
    "15*x5 + 24*x6 >= 66",
    "31*x1 + 24*x6 >= 66",
    "21*x0 + 15*x5 >= 66",
    "28*x2 + 24*x6 >= 66",
    "21*x0 + 3*x7 >= 66",
    "31*x1 + 3*x7 >= 66",
    "21*x0 + 24*x6 >= 66",
    "2*x3 + 3*x7 >= 66",
    "2*x3 + 24*x6 >= 66",
    "31*x1 + 15*x5 >= 66",
    "2*x3 + 15*x5 >= 66",
    "15*x5 + 24*x6 + 3*x7 >= 66",
    "21*x0 + 28*x2 + 15*x5 >= 66",
    "31*x1 + 15*x5 + 3*x7 >= 66",
    "15*x5 + 24*x6 + 3*x7 >= 66",
    "28*x2 + 2*x3 + 3*x7 >= 66",
    "31*x1 + 24*x6 + 3*x7 >= 66",
    "31*x1 + 2*x3 + 15*x5 >= 66",
    "21*x0 + 2*x3 + 15*x5 >= 66",
    "31*x1 + 31*x4 + 15*x5 >= 66",
    "31*x1 + 28*x2 + 2*x3 >= 66",
    "28*x2 + 31*x4 + 3*x7 >= 66",
    "31*x1 + 15*x5 + 24*x6 >= 66",
    "31*x1 + 28*x2 + 3*x7 >= 66",
    "21*x0 + 28*x2 + 31*x4 >= 66",
    "28*x2 + 15*x5 + 3*x7 >= 66",
    "2*x3 + 31*x4 + 24*x6 >= 66",
    "28*x2 + 2*x3 + 15*x5 >= 66",
    "2*x3 + 15*x5 + 3*x7 >= 66",
    "31*x1 + 31*x4 + 3*x7 >= 66",
    "21*x0 + 28*x2 + 2*x3 >= 66",
    "28*x2 + 2*x3 + 24*x6 >= 66",
    "21*x0 + 15*x5 + 24*x6 >= 66",
    "2*x3 + 24*x6 + 3*x7 >= 66",
    "31*x4 + 15*x5 + 3*x7 >= 66",
    "21*x0 + 24*x6 + 3*x7 >= 66",
    "31*x1 + 28*x2 + 31*x4 >= 66",
    "21*x0 + 31*x4 + 3*x7 >= 66",
    "31*x1 + 2*x3 + 3*x7 >= 66",
    "28*x2 + 31*x4 + 24*x6 >= 66",
    "31*x4 + 24*x6 + 3*x7 >= 66",
    "15*x5 + 24*x6 >= 44",
    "31*x1 + 24*x6 >= 44",
    "21*x0 + 15*x5 >= 44",
    "28*x2 + 24*x6 >= 44",
    "21*x0 + 3*x7 >= 44",
    "31*x1 + 3*x7 >= 44",
    "21*x0 + 24*x6 >= 44",
    "2*x3 + 3*x7 >= 44",
    "2*x3 + 24*x6 >= 44",
    "31*x1 + 15*x5 >= 44",
    "2*x3 + 15*x5 >= 44",
    "15*x5 + 24*x6 + 3*x7 >= 44",
    "21*x0 + 28*x2 + 15*x5 >= 44",
    "31*x1 + 15*x5 + 3*x7 >= 44",
    "15*x5 + 24*x6 + 3*x7 >= 44",
    "28*x2 + 2*x3 + 3*x7 >= 44",
    "31*x1 + 24*x6 + 3*x7 >= 44",
    "31*x1 + 2*x3 + 15*x5 >= 44",
    "21*x0 + 2*x3 + 15*x5 >= 44",
    "31*x1 + 31*x4 + 15*x5 >= 44",
    "31*x1 + 28*x2 + 2*x3 >= 44",
    "28*x2 + 31*x4 + 3*x7 >= 44",
    "31*x1 + 15*x5 + 24*x6 >= 44",
    "31*x1 + 28*x2 + 3*x7 >= 44",
    "21*x0 + 28*x2 + 31*x4 >= 44",
    "28*x2 + 15*x5 + 3*x7 >= 44",
    "2*x3 + 31*x4 + 24*x6 >= 44",
    "28*x2 + 2*x3 + 15*x5 >= 44",
    "2*x3 + 15*x5 + 3*x7 >= 44",
    "31*x1 + 31*x4 + 3*x7 >= 44",
    "21*x0 + 28*x2 + 2*x3 >= 44",
    "28*x2 + 2*x3 + 24*x6 >= 44",
    "21*x0 + 15*x5 + 24*x6 >= 44",
    "2*x3 + 24*x6 + 3*x7 >= 44",
    "31*x4 + 15*x5 + 3*x7 >= 44",
    "21*x0 + 24*x6 + 3*x7 >= 44",
    "31*x1 + 28*x2 + 31*x4 >= 44",
    "21*x0 + 31*x4 + 3*x7 >= 44",
    "31*x1 + 2*x3 + 3*x7 >= 44",
    "28*x2 + 31*x4 + 24*x6 >= 44",
    "31*x4 + 24*x6 + 3*x7 >= 44",
    "15*x5 + 24*x6 >= 75",
    "31*x1 + 24*x6 >= 75",
    "21*x0 + 15*x5 >= 75",
    "28*x2 + 24*x6 >= 75",
    "21*x0 + 3*x7 >= 75",
    "31*x1 + 3*x7 >= 75",
    "21*x0 + 24*x6 >= 75",
    "2*x3 + 3*x7 >= 75",
    "2*x3 + 24*x6 >= 75",
    "31*x1 + 15*x5 >= 75",
    "2*x3 + 15*x5 >= 75",
    "15*x5 + 24*x6 + 3*x7 >= 75",
    "21*x0 + 28*x2 + 15*x5 >= 75",
    "31*x1 + 15*x5 + 3*x7 >= 75",
    "15*x5 + 24*x6 + 3*x7 >= 75",
    "28*x2 + 2*x3 + 3*x7 >= 75",
    "31*x1 + 24*x6 + 3*x7 >= 75",
    "31*x1 + 2*x3 + 15*x5 >= 75",
    "21*x0 + 2*x3 + 15*x5 >= 75",
    "31*x1 + 31*x4 + 15*x5 >= 75",
    "31*x1 + 28*x2 + 2*x3 >= 75",
    "28*x2 + 31*x4 + 3*x7 >= 75",
    "31*x1 + 15*x5 + 24*x6 >= 75",
    "31*x1 + 28*x2 + 3*x7 >= 75",
    "21*x0 + 28*x2 + 31*x4 >= 75",
    "28*x2 + 15*x5 + 3*x7 >= 75",
    "2*x3 + 31*x4 + 24*x6 >= 75",
    "28*x2 + 2*x3 + 15*x5 >= 75",
    "2*x3 + 15*x5 + 3*x7 >= 75",
    "31*x1 + 31*x4 + 3*x7 >= 75",
    "21*x0 + 28*x2 + 2*x3 >= 75",
    "28*x2 + 2*x3 + 24*x6 >= 75",
    "21*x0 + 15*x5 + 24*x6 >= 75",
    "2*x3 + 24*x6 + 3*x7 >= 75",
    "31*x4 + 15*x5 + 3*x7 >= 75",
    "21*x0 + 24*x6 + 3*x7 >= 75",
    "31*x1 + 28*x2 + 31*x4 >= 75",
    "21*x0 + 31*x4 + 3*x7 >= 75",
    "31*x1 + 2*x3 + 3*x7 >= 75",
    "28*x2 + 31*x4 + 24*x6 >= 75",
    "31*x4 + 24*x6 + 3*x7 >= 75",
    "15*x5 + 24*x6 >= 43",
    "31*x1 + 24*x6 >= 43",
    "21*x0 + 15*x5 >= 43",
    "28*x2 + 24*x6 >= 43",
    "21*x0 + 3*x7 >= 43",
    "31*x1 + 3*x7 >= 43",
    "21*x0 + 24*x6 >= 43",
    "2*x3 + 3*x7 >= 43",
    "2*x3 + 24*x6 >= 43",
    "31*x1 + 15*x5 >= 43",
    "2*x3 + 15*x5 >= 43",
    "15*x5 + 24*x6 + 3*x7 >= 43",
    "21*x0 + 28*x2 + 15*x5 >= 43",
    "31*x1 + 15*x5 + 3*x7 >= 43",
    "15*x5 + 24*x6 + 3*x7 >= 43",
    "28*x2 + 2*x3 + 3*x7 >= 43",
    "31*x1 + 24*x6 + 3*x7 >= 43",
    "31*x1 + 2*x3 + 15*x5 >= 43",
    "21*x0 + 2*x3 + 15*x5 >= 43",
    "31*x1 + 31*x4 + 15*x5 >= 43",
    "31*x1 + 28*x2 + 2*x3 >= 43",
    "28*x2 + 31*x4 + 3*x7 >= 43",
    "31*x1 + 15*x5 + 24*x6 >= 43",
    "31*x1 + 28*x2 + 3*x7 >= 43",
    "21*x0 + 28*x2 + 31*x4 >= 43",
    "28*x2 + 15*x5 + 3*x7 >= 43",
    "2*x3 + 31*x4 + 24*x6 >= 43",
    "28*x2 + 2*x3 + 15*x5 >= 43",
    "2*x3 + 15*x5 + 3*x7 >= 43",
    "31*x1 + 31*x4 + 3*x7 >= 43",
    "21*x0 + 28*x2 + 2*x3 >= 43",
    "28*x2 + 2*x3 + 24*x6 >= 43",
    "21*x0 + 15*x5 + 24*x6 >= 43",
    "2*x3 + 24*x6 + 3*x7 >= 43",
    "31*x4 + 15*x5 + 3*x7 >= 43",
    "21*x0 + 24*x6 + 3*x7 >= 43",
    "31*x1 + 28*x2 + 31*x4 >= 43",
    "21*x0 + 31*x4 + 3*x7 >= 43",
    "31*x1 + 2*x3 + 3*x7 >= 43",
    "28*x2 + 31*x4 + 24*x6 >= 43",
    "31*x4 + 24*x6 + 3*x7 >= 43",
    "15*x5 + 24*x6 >= 58",
    "31*x1 + 24*x6 >= 58",
    "21*x0 + 15*x5 >= 58",
    "28*x2 + 24*x6 >= 58",
    "21*x0 + 3*x7 >= 58",
    "31*x1 + 3*x7 >= 58",
    "21*x0 + 24*x6 >= 58",
    "2*x3 + 3*x7 >= 58",
    "2*x3 + 24*x6 >= 58",
    "31*x1 + 15*x5 >= 58",
    "2*x3 + 15*x5 >= 58",
    "15*x5 + 24*x6 + 3*x7 >= 58",
    "21*x0 + 28*x2 + 15*x5 >= 58",
    "31*x1 + 15*x5 + 3*x7 >= 58",
    "15*x5 + 24*x6 + 3*x7 >= 58",
    "28*x2 + 2*x3 + 3*x7 >= 58",
    "31*x1 + 24*x6 + 3*x7 >= 58",
    "31*x1 + 2*x3 + 15*x5 >= 58",
    "21*x0 + 2*x3 + 15*x5 >= 58",
    "31*x1 + 31*x4 + 15*x5 >= 58",
    "31*x1 + 28*x2 + 2*x3 >= 58",
    "28*x2 + 31*x4 + 3*x7 >= 58",
    "31*x1 + 15*x5 + 24*x6 >= 58",
    "31*x1 + 28*x2 + 3*x7 >= 58",
    "21*x0 + 28*x2 + 31*x4 >= 58",
    "28*x2 + 15*x5 + 3*x7 >= 58",
    "2*x3 + 31*x4 + 24*x6 >= 58",
    "28*x2 + 2*x3 + 15*x5 >= 58",
    "2*x3 + 15*x5 + 3*x7 >= 58",
    "31*x1 + 31*x4 + 3*x7 >= 58",
    "21*x0 + 28*x2 + 2*x3 >= 58",
    "28*x2 + 2*x3 + 24*x6 >= 58",
    "21*x0 + 15*x5 + 24*x6 >= 58",
    "2*x3 + 24*x6 + 3*x7 >= 58",
    "31