```json
{
  "sym_variables": [
    ("x0", "hours worked by Laura"),
    ("x1", "hours worked by Peggy"),
    ("x2", "hours worked by Bill"),
    ("x3", "hours worked by Paul"),
    ("x4", "hours worked by Bobby"),
    ("x5", "hours worked by John"),
    ("x6", "hours worked by Dale")
  ],
  "objective_function": "3.01*x0 + 6.58*x1 + 7.99*x2 + 7.29*x3 + 3.94*x4 + 8.65*x5 + 8.16*x6",
  "constraints": [
    "3*x3 + 5*x6 >= 35",
    "11*x4 + 3*x5 >= 53",
    "3*x3 + 3*x5 >= 46",
    "13*x1 + 3*x5 >= 67",
    "13*x1 + 5*x6 >= 67",
    "23*x0 + 13*x1 + 3*x5 >= 39",
    "23*x0 + 12*x2 + 3*x3 >= 39",
    "23*x0 + 3*x3 + 11*x4 >= 39",
    "13*x1 + 12*x2 + 11*x4 >= 39",
    "3*x3 + 11*x4 + 3*x5 >= 39",
    "23*x0 + 13*x1 + 5*x6 >= 39",
    "23*x0 + 12*x2 + 11*x4 >= 39",
    "13*x1 + 11*x4 + 5*x6 >= 39",
    "23*x0 + 12*x2 + 3*x5 >= 39",
    "13*x1 + 3*x3 + 5*x6 >= 39",
    "12*x2 + 3*x3 + 3*x5 >= 39",
    "12*x2 + 3*x3 + 5*x6 >= 39",
    "23*x0 + 13*x1 + 3*x3 >= 39",
    "13*x1 + 3*x3 + 3*x5 >= 39",
    "13*x1 + 12*x2 + 5*x6 >= 39",
    "12*x2 + 3*x3 + 11*x4 >= 39",
    "23*x0 + 3*x5 + 5*x6 >= 39",
    "13*x1 + 3*x3 + 11*x4 >= 39",
    "23*x0 + 13*x1 + 11*x4 >= 39",
    "23*x0 + 3*x3 + 3*x5 >= 39",
    "23*x0 + 13*x1 + 3*x5 >= 48",
    "23*x0 + 12*x2 + 3*x3 >= 48",
    "23*x0 + 3*x3 + 11*x4 >= 48",
    "13*x1 + 12*x2 + 11*x4 >= 48",
    "3*x3 + 11*x4 + 3*x5 >= 48",
    "23*x0 + 13*x1 + 5*x6 >= 48",
    "23*x0 + 12*x2 + 11*x4 >= 48",
    "13*x1 + 11*x4 + 5*x6 >= 48",
    "23*x0 + 12*x2 + 3*x5 >= 48",
    "13*x1 + 3*x3 + 5*x6 >= 48",
    "12*x2 + 3*x3 + 3*x5 >= 48",
    "12*x2 + 3*x3 + 5*x6 >= 48",
    "23*x0 + 13*x1 + 3*x3 >= 48",
    "13*x1 + 3*x3 + 3*x5 >= 48",
    "13*x1 + 12*x2 + 5*x6 >= 48",
    "12*x2 + 3*x3 + 11*x4 >= 48",
    "23*x0 + 3*x5 + 5*x6 >= 48",
    "13*x1 + 3*x3 + 11*x4 >= 48",
    "23*x0 + 13*x1 + 11*x4 >= 48",
    "23*x0 + 3*x3 + 3*x5 >= 48",
    "23*x0 + 13*x1 + 3*x5 >= 51",
    "23*x0 + 12*x2 + 3*x3 >= 51",
    "23*x0 + 3*x3 + 11*x4 >= 51",
    "13*x1 + 12*x2 + 11*x4 >= 51",
    "3*x3 + 11*x4 + 3*x5 >= 51",
    "23*x0 + 13*x1 + 5*x6 >= 51",
    "23*x0 + 12*x2 + 11*x4 >= 51",
    "13*x1 + 11*x4 + 5*x6 >= 51",
    "23*x0 + 12*x2 + 3*x5 >= 51",
    "13*x1 + 3*x3 + 5*x6 >= 51",
    "12*x2 + 3*x3 + 3*x5 >= 51",
    "12*x2 + 3*x3 + 5*x6 >= 51",
    "23*x0 + 13*x1 + 3*x3 >= 51",
    "13*x1 + 3*x3 + 3*x5 >= 51",
    "13*x1 + 12*x2 + 5*x6 >= 51",
    "12*x2 + 3*x3 + 11*x4 >= 51",
    "23*x0 + 3*x5 + 5*x6 >= 51",
    "13*x1 + 3*x3 + 11*x4 >= 51",
    "23*x0 + 13*x1 + 11*x4 >= 51",
    "23*x0 + 3*x3 + 3*x5 >= 51",
    "23*x0 + 13*x1 + 3*x5 >= 52",
    "23*x0 + 12*x2 + 3*x3 >= 52",
    "23*x0 + 3*x3 + 11*x4 >= 52",
    "13*x1 + 12*x2 + 11*x4 >= 52",
    "3*x3 + 11*x4 + 3*x5 >= 52",
    "23*x0 + 13*x1 + 5*x6 >= 52",
    "23*x0 + 12*x2 + 11*x4 >= 52",
    "13*x1 + 11*x4 + 5*x6 >= 52",
    "23*x0 + 12*x2 + 3*x5 >= 52",
    "13*x1 + 3*x3 + 5*x6 >= 52",
    "12*x2 + 3*x3 + 3*x5 >= 52",
    "12*x2 + 3*x3 + 5*x6 >= 52",
    "23*x0 + 13*x1 + 3*x3 >= 52",
    "13*x1 + 3*x3 + 3*x5 >= 52",
    "13*x1 + 12*x2 + 5*x6 >= 52",
    "12*x2 + 3*x3 + 11*x4 >= 52",
    "23*x0 + 3*x5 + 5*x6 >= 52",
    "13*x1 + 3*x3 + 11*x4 >= 52",
    "23*x0 + 13*x1 + 11*x4 >= 52",
    "23*x0 + 3*x3 + 3*x5 >= 52",
    "23*x0 + 13*x1 + 3*x5 >= 63",
    "23*x0 + 12*x2 + 3*x3 >= 63",
    "23*x0 + 3*x3 + 11*x4 >= 63",
    "13*x1 + 12*x2 + 11*x4 >= 63",
    "3*x3 + 11*x4 + 3*x5 >= 63",
    "23*x0 + 13*x1 + 5*x6 >= 63",
    "23*x0 + 12*x2 + 11*x4 >= 63",
    "13*x1 + 11*x4 + 5*x6 >= 63",
    "23*x0 + 12*x2 + 3*x5 >= 63",
    "13*x1 + 3*x3 + 5*x6 >= 63",
    "12*x2 + 3*x3 + 3*x5 >= 63",
    "12*x2 + 3*x3 + 5*x6 >= 63",
    "23*x0 + 13*x1 + 3*x3 >= 63",
    "13*x1 + 3*x3 + 3*x5 >= 63",
    "13*x1 + 12*x2 + 5*x6 >= 63",
    "12*x2 + 3*x3 + 11*x4 >= 63",
    "23*x0 + 3*x5 + 5*x6 >= 63",
    "13*x1 + 3*x3 + 11*x4 >= 63",
    "23*x0 + 13*x1 + 11*x4 >= 63",
    "23*x0 + 3*x3 + 3*x5 >= 63",
    "23*x0 + 13*x1 + 3*x5 >= 40",
    "23*x0 + 12*x2 + 3*x3 >= 40",
    "23*x0 + 3*x3 + 11*x4 >= 40",
    "13*x1 + 12*x2 + 11*x4 >= 40",
    "3*x3 + 11*x4 + 3*x5 >= 40",
    "23*x0 + 13*x1 + 5*x6 >= 40",
    "23*x0 + 12*x2 + 11*x4 >= 40",
    "13*x1 + 11*x4 + 5*x6 >= 40",
    "23*x0 + 12*x2 + 3*x5 >= 40",
    "13*x1 + 3*x3 + 5*x6 >= 40",
    "12*x2 + 3*x3 + 3*x5 >= 40",
    "12*x2 + 3*x3 + 5*x6 >= 40",
    "23*x0 + 13*x1 + 3*x3 >= 40",
    "13*x1 + 3*x3 + 3*x5 >= 40",
    "13*x1 + 12*x2 + 5*x6 >= 40",
    "12*x2 + 3*x3 + 11*x4 >= 40",
    "23*x0 + 3*x5 + 5*x6 >= 40",
    "13*x1 + 3*x3 + 11*x4 >= 40",
    "23*x0 + 13*x1 + 11*x4 >= 40",
    "23*x0 + 3*x3 + 3*x5 >= 40",
    "23*x0 + 13*x1 + 3*x5 >= 56",
    "23*x0 + 12*x2 + 3*x3 >= 56",
    "23*x0 + 3*x3 + 11*x4 >= 56",
    "13*x1 + 12*x2 + 11*x4 >= 56",
    "3*x3 + 11*x4 + 3*x5 >= 56",
    "23*x0 + 13*x1 + 5*x6 >= 56",
    "23*x0 + 12*x2 + 11*x4 >= 56",
    "13*x1 + 11*x4 + 5*x6 >= 56",
    "23*x0 + 12*x2 + 3*x5 >= 56",
    "13*x1 + 3*x3 + 5*x6 >= 56",
    "12*x2 + 3*x3 + 3*x5 >= 56",
    "12*x2 + 3*x3 + 5*x6 >= 56",
    "23*x0 + 13*x1 + 3*x3 >= 56",
    "13*x1 + 3*x3 + 3*x5 >= 56",
    "13*x1 + 12*x2 + 5*x6 >= 56",
    "12*x2 + 3*x3 + 11*x4 >= 56",
    "23*x0 + 3*x5 + 5*x6 >= 56",
    "13*x1 + 3*x3 + 11*x4 >= 56",
    "23*x0 + 13*x1 + 11*x4 >= 56",
    "23*x0 + 3*x3 + 3*x5 >= 56",
    "23*x0 + 13*x1 + 3*x5 >= 59",
    "23*x0 + 12*x2 + 3*x3 >= 59",
    "23*x0 + 3*x3 + 11*x4 >= 59",
    "13*x1 + 12*x2 + 11*x4 >= 59",
    "3*x3 + 11*x4 + 3*x5 >= 59",
    "23*x0 + 13*x1 + 5*x6 >= 59",
    "23*x0 + 12*x2 + 11*x4 >= 59",
    "13*x1 + 11*x4 + 5*x6 >= 59",
    "23*x0 + 12*x2 + 3*x5 >= 59",
    "13*x1 + 3*x3 + 5*x6 >= 59",
    "12*x2 + 3*x3 + 3*x5 >= 59",
    "12*x2 + 3*x3 + 5*x6 >= 59",
    "23*x0 + 13*x1 + 3*x3 >= 59",
    "13*x1 + 3*x3 + 3*x5 >= 59",
    "13*x1 + 12*x2 + 5*x6 >= 59",
    "12*x2 + 3*x3 + 11*x4 >= 59",
    "23*x0 + 3*x5 + 5*x6 >= 59",
    "13*x1 + 3*x3 + 11*x4 >= 59",
    "23*x0 + 13*x1 + 11*x4 >= 59",
    "23*x0 + 3*x3 + 3*x5 >= 59",
    "23*x0 + 13*x1 + 3*x5 >= 50",
    "23*x0 + 12*x2 + 3*x3 >= 50",
    "23*x0 + 3*x3 + 11*x4 >= 50",
    "13*x1 + 12*x2 + 11*x4 >= 50",
    "3*x3 + 11*x4 + 3*x5 >= 50",
    "23*x0 + 13*x1 + 5*x6 >= 50",
    "23*x0 + 12*x2 + 11*x4 >= 50",
    "13*x1 + 11*x4 + 5*x6 >= 50",
    "23*x0 + 12*x2 + 3*x5 >= 50",
    "13*x1 + 3*x3 + 5*x6 >= 50",
    "12*x2 + 3*x3 + 3*x5 >= 50",
    "12*x2 + 3*x3 + 5*x6 >= 50",
    "23*x0 + 13*x1 + 3*x3 >= 50",
    "13*x1 + 3*x3 + 3*x5 >= 50",
    "13*x1 + 12*x2 + 5*x6 >= 50",
    "12*x2 + 3*x3 + 11*x4 >= 50",
    "23*x0 + 3*x5 + 5*x6 >= 50",
    "13*x1 + 3*x3 + 11*x4 >= 50",
    "23*x0 + 13*x1 + 11*x4 >= 50",
    "23*x0 + 3*x3 + 3*x5 >= 50",
    "23*x0 + 13*x1 + 3*x5 >= 38",
    "23*x0 + 12*x2 + 3*x3 >= 38",
    "23*x0 + 3*x3 + 11*x4 >= 38",
    "13*x1 + 12*x2 + 11*x4 >= 38",
    "3*x3 + 11*x4 + 3*x5 >= 38",
    "23*x0 + 13*x1 + 5*x6 >= 38",
    "23*x0 + 12*x2 + 11*x4 >= 38",
    "13*x1 + 11*x4 + 5*x6 >= 38",
    "23*x0 + 12*x2 + 3*x5 >= 38",
    "13*x1 + 3*x3 + 5*x6 >= 38",
    "12*x2 + 3*x3 + 3*x5 >= 38",
    "12*x2 + 3*x3 + 5*x6 >= 38",
    "23*x0 + 13*x1 + 3*x3 >= 38",
    "13*x1 + 3*x3 + 3*x5 >= 38",
    "13*x1 + 12*x2 + 5*x6 >= 38",
    "12*x2 + 3*x3 + 11*x4 >= 38",
    "23*x0 + 3*x5 + 5*x6 >= 38",
    "13*x1 + 3*x3 + 11*x4 >= 38",
    "23*x0 + 13*x1 + 11*x4 >= 38",
    "23*x0 + 3*x3 + 3*x5 >= 38",
    "23*x0 + 13*x1 + 3*x5 >= 51",
    "23*x0 + 12*x2 + 3*x3 >= 51",
    "23*x0 + 3*x3 + 11*x4 >= 51",
    "13*x1 + 12*x2 + 11*x4 >= 51",
    "3*x3 + 11*x4 + 3*x5 >= 51",
    "23*x0 + 13*x1 + 5*x6 >= 51",
    "23*x0 + 12*x2 + 11*x4 >= 51",
    "13*x1 + 11*x4 + 5*x6 >= 51",
    "23*x0 + 12*x2 + 3*x5 >= 51",
    "13*x1 + 3*x3 + 5*x6 >= 51",
    "12*x2 + 3*x3 + 3*x5 >= 51",
    "12*x2 + 3*x3 + 5*x6 >= 51",
    "23*x0 + 13*x1 + 3*x3 >= 51",
    "13*x1 + 3*x3 + 3*x5 >= 51",
    "13*x1 + 12*x2 + 5*x6 >= 51",
    "12*x2 + 3*x3 + 11*x4 >= 51",
    "23*x0 + 3*x5 + 5*x6 >= 51",
    "13*x1 + 3*x3 + 11*x4 >= 51",
    "23*x0 + 13*x1 + 11*x4 >= 51",
    "23*x0 + 3*x3 + 3*x5 >= 51",
    "23*x0 + 13*x1 + 3*x5 >= 66",
    "23*x0 + 12*x2 + 3*x3 >= 66",
    "23*x0 + 3*x3 + 11*x4 >= 66",
    "13*x1 + 12*x2 + 11*x4 >= 66",
    "3*x3 + 11*x4 + 3*x5 >= 66",
    "23*x0 + 13*x1 + 5*x6 >= 66",
    "23*x0 + 12*x2 + 11*x4 >= 66",
    "13*x1 + 11*x4 + 5*x6 >= 66",
    "23*x0 + 12*x2 + 3*x5 >= 66",
    "13*x1 + 3*x3 + 5*x6 >= 66",
    "12*x2 + 3*x3 + 3*x5 >= 66",
    "12*x2 + 3*x3 + 5*x6 >= 66",
    "23*x0 + 13*x1 + 3*x3 >= 66",
    "13*x1 + 3*x3 + 3*x5 >= 66",
    "13*x1 + 12*x2 + 5*x6 >= 66",
    "12*x2 + 3*x3 + 11*x4 >= 66",
    "23*x0 + 3*x5 + 5*x6 >= 66",
    "13*x1 + 3*x3 + 11*x4 >= 66",
    "23*x0 + 13*x1 + 11*x4 >= 66",
    "23*x0 + 3*x3 + 3*x5 >= 66",
    "23*x0 + 13*x1 + 3*x5 >= 66",
    "23*x0 + 12*x2 + 3*x3 >= 66",
    "23*x0 + 3*x3 + 11*x4 >= 66",
    "13*x1 + 12*x2 + 11*x4 >= 66",
    "3*x3 + 11*x4 + 3*x5 >= 66",
    "23*x0 + 13*x1 + 5*x6 >= 66",
    "23*x0 + 12*x2 + 11*x4 >= 66",
    "13*x1 + 11*x4 + 5*x6 >= 66",
    "23*x0 + 12*x2 + 3*x5 >= 66",
    "13*x1 + 3*x3 + 5*x6 >= 66",
    "12*x2 + 3*x3 + 3*x5 >= 66",
    "12*x2 + 3*x3 + 5*x6 >= 66",
    "23*x0 + 13*x1 + 3*x3 >= 66",
    "13*x1 + 3*x3 + 3*x5 >= 66",
    "13*x1 + 12*x2 + 5*x6 >= 66",
    "12*x2 + 3*x3 + 11*x4 >= 66",
    "23*x0 + 3*x5 + 5*x6 >= 66",
    "13*x1 + 3*x3 + 11*x4 >= 66",
    "23*x0 + 13*x1 + 11*x4 >= 66",
    "23*x0 + 3*x3 + 3*x5 >= 66",
    "23*x0 + 13*x1 + 3*x5 >= 62",
    "23*x0 + 12*x2 + 3*x3 >= 62",
    "23*x0 + 3*x3 + 11*x4 >= 62",
    "13*x1 + 12*x2 + 11*x4 >= 62",
    "3*x3 + 11*x4 + 3*x5 >= 62",
    "23*x0 + 13*x1 + 5*x6 >= 62",
    "23*x0 + 12*x2 + 11*x4 >= 62",
    "13*x1 + 11*x4 + 5*x6 >= 62",
    "23*x0 + 12*x2 + 3*x5 >= 62",
    "13*x1 + 3*x3 + 5*x6 >= 62",
    "12*x2 + 3*x3 + 3*x5 >= 62",
    "12*x2 + 3*x3 + 5*x6 >= 62",
    "23*x0 + 13*x1 + 3*x3 >= 62",
    "13*x1 + 3*x3 + 3*x5 >= 62",
    "13*x1 + 12*x2 + 5*x6 >= 62",
    "12*x2 + 3*x3 + 11*x4 >= 62",
    "23*x0 + 3*x5 + 5*x6 >= 62",
    "13*x1 + 3*x3 + 11*x4 >= 62",
    "23*x0 + 13*x1 + 11*x4 >= 62",
    "23*x0 + 3*x3 + 3*x5 >= 62",
    "23*x0 + 13*x1 + 3*x5 >= 57",
    "23*x0 + 12*x2 + 3*x3 >= 57",
    "23*x0 + 3*x3 + 11*x4 >= 57",
    "13*x1 + 12*x2 + 11*x4 >= 57",
    "3*x3 + 11*x4 + 3*x5 >= 57",
    "23*x0 + 13*x1 + 5*x6 >= 57",
    "23*x0 + 12*x2 + 11*x4 >= 57",
    "13*x1 + 11*x4 + 5*x6 >= 57",
    "23*x0 + 12*x2 + 3*x5 >= 57",
    "13*x1 + 3*x3 + 5*x6 >= 57",
    "12*x2 + 3*x3 + 3*x5 >= 57",
    "12*x2 + 3*x3 + 5*x6 >= 57",
    "23*x0 + 13*x1 + 3*x3 >= 57",
    "13*x1 + 3*x3 + 3*x5 >= 57",
    "13*x1 + 12*x2 + 5*x6 >= 57",
    "12*x2 + 3*x3 + 11*x4 >= 57",
    "23*x0 + 3*x5 + 5*x6 >= 57",
    "13*x1 + 3*x3 + 11*x4 >= 57",
    "23*x0 + 13*x1 + 11*x4 >= 57",
    "23*x0 + 3*x3 + 3*x5 >= 57",
    "23*x0 + 13*x1 + 3*x5 >= 46",
    "23*x0 + 12*x2 + 3*x3 >= 46",
    "23*x0 + 3*x3 + 11*x4 >= 46",
    "13*x1 + 12*x2 + 11*x4 >= 46",
    "3*x3 + 11*x4 + 3*x5 >= 46",
    "23*x0 + 13*x1 + 5*x6 >= 46",
    "23*x0 + 12*x2 + 11*x4 >= 46",
