```json
{
  "sym_variables": [
    ("x0", "hours worked by Dale"),
    ("x1", "hours worked by Peggy"),
    ("x2", "hours worked by Hank"),
    ("x3", "hours worked by John"),
    ("x4", "hours worked by Mary"),
    ("x5", "hours worked by Laura")
  ],
  "objective_function": "6.9*x0 + 5.6*x1 + 8.76*x2 + 5.63*x3 + 2.6*x4 + 2.4*x5",
  "constraints": [
    "12*x0 + 10*x3 >= 21",
    "12*x0 + 12*x4 >= 12",
    "13*x1 + 2*x2 >= 15",
    "12*x0 + 7*x5 >= 10",
    "12*x4 + 7*x5 >= 23",
    "2*x2 + 12*x4 >= 19",
    "2*x2 + 7*x5 >= 18",
    "13*x1 + 12*x4 >= 11",
    "12*x0 + 2*x2 >= 18",
    "12*x0 + 13*x1 + 2*x2 + 10*x3 + 12*x4 + 7*x5 >= 18",
    "5*x0 + 15*x5 >= 37",
    "12*x2 + 5*x3 >= 21",
    "2*x4 + 15*x5 >= 20",
    "3*x1 + 15*x5 >= 23",
    "3*x1 + 5*x3 >= 26",
    "12*x2 + 2*x4 >= 31",
    "12*x2 + 15*x5 >= 15",
    "5*x0 + 5*x3 >= 15",
    "5*x3 + 2*x4 >= 27",
    "5*x0 + 12*x2 >= 17",
    "3*x1 + 2*x4 >= 32",
    "5*x0 + 3*x1 + 12*x2 >= 30",
    "12*x2 + 5*x3 + 2*x4 >= 30",
    "3*x1 + 12*x2 + 5*x3 >= 30",
    "5*x0 + 2*x4 + 15*x5 >= 30",
    "3*x1 + 12*x2 + 2*x4 >= 30",
    "5*x3 + 2*x4 + 15*x5 >= 30",
    "5*x0 + 5*x3 + 15*x5 >= 30",
    "12*x2 + 5*x3 + 15*x5 >= 30",
    "5*x0 + 3*x1 + 12*x2 >= 30", 
    "12*x2 + 5*x3 + 2*x4 >= 30",
    "3*x1 + 12*x2 + 5*x3 >= 30",
    "5*x0 + 2*x4 + 15*x5 >= 30",
    "3*x1 + 12*x2 + 2*x4 >= 30",
    "5*x3 + 2*x4 + 15*x5 >= 30",
    "5*x0 + 5*x3 + 15*x5 >= 30",
    "12*x2 + 5*x3 + 15*x5 >= 30",
    "5*x0 + 3*x1 + 12*x2 >= 19",
    "12*x2 + 5*x3 + 2*x4 >= 19",
    "3*x1 + 12*x2 + 5*x3 >= 19",
    "5*x0 + 2*x4 + 15*x5 >= 19",
    "3*x1 + 12*x2 + 2*x4 >= 19",
    "5*x3 + 2*x4 + 15*x5 >= 19",
    "5*x0 + 5*x3 + 15*x5 >= 19",
    "12*x2 + 5*x3 + 15*x5 >= 19",
    "5*x0 + 3*x1 + 12*x2 >= 25",
    "12*x2 + 5*x3 + 2*x4 >= 25",
    "3*x1 + 12*x2 + 5*x3 >= 25",
    "5*x0 + 2*x4 + 15*x5 >= 25",
    "3*x1 + 12*x2 + 2*x4 >= 25",
    "5*x3 + 2*x4 + 15*x5 >= 25",
    "5*x0 + 5*x3 + 15*x5 >= 25",
    "12*x2 + 5*x3 + 15*x5 >= 25",
    "5*x0 + 3*x1 + 12*x2 >= 35",
    "12*x2 + 5*x3 + 2*x4 >= 35",
    "3*x1 + 12*x2 + 5*x3 >= 35",
    "5*x0 + 2*x4 + 15*x5 >= 35",
    "3*x1 + 12*x2 + 2*x4 >= 35",
    "5*x3 + 2*x4 + 15*x5 >= 35",
    "5*x0 + 5*x3 + 15*x5 >= 35",
    "12*x2 + 5*x3 + 15*x5 >= 35",
    "5*x0 + 3*x1 + 12*x2 >= 24",
    "12*x2 + 5*x3 + 2*x4 >= 24",
    "3*x1 + 12*x2 + 5*x3 >= 24",
    "5*x0 + 2*x4 + 15*x5 >= 24",
    "3*x1 + 12*x2 + 2*x4 >= 24",
    "5*x3 + 2*x4 + 15*x5 >= 24",
    "5*x0 + 5*x3 + 15*x5 >= 24",
    "12*x2 + 5*x3 + 15*x5 >= 24",
    "5*x0 + 3*x1 + 12*x2 >= 36",
    "12*x2 + 5*x3 + 2*x4 >= 36",
    "3*x1 + 12*x2 + 5*x3 >= 36",
    "5*x0 + 2*x4 + 15*x5 >= 36",
    "3*x1 + 12*x2 + 2*x4 >= 36",
    "5*x3 + 2*x4 + 15*x5 >= 36",
    "5*x0 + 5*x3 + 15*x5 >= 36",
    "12*x2 + 5*x3 + 15*x5 >= 36",
    "5*x0 + 3*x1 + 12*x2 >= 32",
    "12*x2 + 5*x3 + 2*x4 >= 32",
    "3*x1 + 12*x2 + 5*x3 >= 32",
    "5*x0 + 2*x4 + 15*x5 >= 32",
    "3*x1 + 12*x2 + 2*x4 >= 32",
    "5*x3 + 2*x4 + 15*x5 >= 32",
    "5*x0 + 5*x3 + 15*x5 >= 32",
    "12*x2 + 5*x3 + 15*x5 >= 32",
    "5*x0 + 3*x1 + 12*x2 + 5*x3 + 2*x4 + 15*x5 >= 32",
    "x3 + 7*x4 >= 12",
    "7*x4 + 10*x5 >= 19",
    "5*x2 + 10*x5 >= 31",
    "4*x1 + 10*x5 >= 17",
    "9*x0 + 7*x4 >= 28",
    "9*x0 + 4*x1 + x3 >= 21",
    "9*x0 + 5*x2 + x3 >= 21",
    "9*x0 + 4*x1 + 7*x4 >= 21",
    "4*x1 + 5*x2 + 10*x5 >= 21",
    "x3 + 7*x4 + 10*x5 >= 21",
    "4*x1 + 7*x4 + 10*x5 >= 21",
    "9*x0 + 7*x4 + 10*x5 >= 21",
    "9*x0 + 5*x2 + 7*x4 >= 21",
    "9*x0 + 4*x1 + 10*x5 >= 21",
    "9*x0 + x3 + 10*x5 >= 21",
    "9*x0 + 4*x1 + x3 >= 26",
    "9*x0 + 5*x2 + x3 >= 26",
    "9*x0 + 4*x1 + 7*x4 >= 26",
    "4*x1 + 5*x2 + 10*x5 >= 26",
    "x3 + 7*x4 + 10*x5 >= 26",
    "4*x1 + 7*x4 + 10*x5 >= 26",
    "9*x0 + 7*x4 + 10*x5 >= 26",
    "9*x0 + 5*x2 + 7*x4 >= 26",
    "9*x0 + 4*x1 + 10*x5 >= 26",
    "9*x0 + x3 + 10*x5 >= 26",
    "9*x0 + 4*x1 + x3 >= 29",
    "9*x0 + 5*x2 + x3 >= 29",
    "9*x0 + 4*x1 + 7*x4 >= 29",
    "4*x1 + 5*x2 + 10*x5 >= 29",
    "x3 + 7*x4 + 10*x5 >= 29",
    "4*x1 + 7*x4 + 10*x5 >= 29",
    "9*x0 + 7*x4 + 10*x5 >= 29",
    "9*x0 + 5*x2 + 7*x4 >= 29",
    "9*x0 + 4*x1 + 10*x5 >= 29",
    "9*x0 + x3 + 10*x5 >= 29",
    "9*x0 + 4*x1 + x3 >= 26",
    "9*x0 + 5*x2 + x3 >= 26",
    "9*x0 + 4*x1 + 7*x4 >= 26",
    "4*x1 + 5*x2 + 10*x5 >= 26",
    "x3 + 7*x4 + 10*x5 >= 26",
    "4*x1 + 7*x4 + 10*x5 >= 26",
    "9*x0 + 7*x4 + 10*x5 >= 26",
    "9*x0 + 5*x2 + 7*x4 >= 26",
    "9*x0 + 4*x1 + 10*x5 >= 26",
    "9*x0 + x3 + 10*x5 >= 26",
    "9*x0 + 4*x1 + x3 >= 20",
    "9*x0 + 5*x2 + x3 >= 20",
    "9*x0 + 4*x1 + 7*x4 >= 20",
    "4*x1 + 5*x2 + 10*x5 >= 20",
    "x3 + 7*x4 + 10*x5 >= 20",
    "4*x1 + 7*x4 + 10*x5 >= 20",
    "9*x0 + 7*x4 + 10*x5 >= 20",
    "9*x0 + 5*x2 + 7*x4 >= 20",
    "9*x0 + 4*x1 + 10*x5 >= 20",
    "9*x0 + x3 + 10*x5 >= 20",
    "9*x0 + 4*x1 + x3 >= 19",
    "9*x0 + 5*x2 + x3 >= 19",
    "9*x0 + 4*x1 + 7*x4 >= 19",
    "4*x1 + 5*x2 + 10*x5 >= 19",
    "x3 + 7*x4 + 10*x5 >= 19",
    "4*x1 + 7*x4 + 10*x5 >= 19",
    "9*x0 + 7*x4 + 10*x5 >= 19",
    "9*x0 + 5*x2 + 7*x4 >= 19",
    "9*x0 + 4*x1 + 10*x5 >= 19",
    "9*x0 + x3 + 10*x5 >= 19",
    "9*x0 + 4*x1 + x3 >= 34",
    "9*x0 + 5*x2 + x3 >= 34",
    "9*x0 + 4*x1 + 7*x4 >= 34",
    "4*x1 + 5*x2 + 10*x5 >= 34",
    "x3 + 7*x4 + 10*x5 >= 34",
    "4*x1 + 7*x4 + 10*x5 >= 34",
    "9*x0 + 7*x4 + 10*x5 >= 34",
    "9*x0 + 5*x2 + 7*x4 >= 34",
    "9*x0 + 4*x1 + 10*x5 >= 34",
    "9*x0 + x3 + 10*x5 >= 34",
    "9*x0 + 4*x1 + x3 >= 34",
    "9*x0 + 5*x2 + x3 >= 34",
    "9*x0 + 4*x1 + 7*x4 >= 34",
    "4*x1 + 5*x2 + 10*x5 >= 34",
    "x3 + 7*x4 + 10*x5 >= 34",
    "4*x1 + 7*x4 + 10*x5 >= 34",
    "9*x0 + 7*x4 + 10*x5 >= 34",
    "9*x0 + 5*x2 + 7*x4 >= 34",
    "9*x0 + 4*x1 + 10*x5 >= 34",
    "9*x0 + x3 + 10*x5 >= 34",
    "9*x0 + 4*x1 + x3 >= 23",
    "9*x0 + 5*x2 + x3 >= 23",
    "9*x0 + 4*x1 + 7*x4 >= 23",
    "4*x1 + 5*x2 + 10*x5 >= 23",
    "x3 + 7*x4 + 10*x5 >= 23",
    "4*x1 + 7*x4 + 10*x5 >= 23",
    "9*x0 + 7*x4 + 10*x5 >= 23",
    "9*x0 + 5*x2 + 7*x4 >= 23",
    "9*x0 + 4*x1 + 10*x5 >= 23",
    "9*x0 + x3 + 10*x5 >= 23",
    "9*x0 + 4*x1 + x3 >= 27",
    "9*x0 + 5*x2 + x3 >= 27",
    "9*x0 + 4*x1 + 7*x4 >= 27",
    "4*x1 + 5*x2 + 10*x5 >= 27",
    "x3 + 7*x4 + 10*x5 >= 27",
    "4*x1 + 7*x4 + 10*x5 >= 27",
    "9*x0 + 7*x4 + 10*x5 >= 27",
    "9*x0 + 5*x2 + 7*x4 >= 27",
    "9*x0 + 4*x1 + 10*x5 >= 27",
    "9*x0 + x3 + 10*x5 >= 27",
    "9*x0 + 4*x1 + 5*x2 + x3 + 7*x4 + 10*x5 >= 27",
    "2*x0 + 14*x2 >= 14",
    "2*x0 + 4*x3 >= 22",
    "3*x1 + 10*x4 >= 15",
    "14*x2 + 4*x3 >= 42",
    "3*x1 + 14*x2 >= 18",
    "14*x2 + 15*x5 >= 14",
    "2*x0 + 15*x5 >= 27",
    "2*x0 + 4*x3 + 15*x5 >= 37",
    "2*x0 + 4*x3 + 10*x4 >= 37",
    "14*x2 + 4*x3 + 10*x4 >= 37",
    "3*x1 + 14*x2 + 15*x5 >= 37",
    "3*x1 + 14*x2 + 10*x4 >= 37",
    "2*x0 + 3*x1 + 15*x5 >= 37",
    "2*x0 + 14*x2 + 15*x5 >= 37",
    "3*x1 + 10*x4 + 15*x5 >= 37",
    "3*x1 + 4*x3 + 10*x4 >= 37",
    "3*x1 + 4*x3 + 15*x5 >= 37",
    "3*x1 + 14*x2 + 4*x3 >= 37",
    "2*x0 + 3*x1 + 4*x3 >= 37",
    "2*x0 + 3*x1 + 14*x2 >= 37",
    "2*x0 + 10*x4 + 15*x5 >= 37",
    "4*x3 + 10*x4 + 15*x5 >= 37",
    "2*x0 + 14*x2 + 10*x4 >= 37",
    "14*x2 + 10*x4 + 15*x5 >= 37",
    "2*x0 + 4*x3 + 15*x5 >= 38",
    "2*x0 + 4*x3 + 10*x4 >= 38",
    "14*x2 + 4*x3 + 10*x4 >= 38",
    "3*x1 + 14*x2 + 15*x5 >= 38",
    "3*x1 + 14*x2 + 10*x4 >= 38",
    "2*x0 + 3*x1 + 15*x5 >= 38",
    "2*x0 + 14*x2 + 15*x5 >= 38",
    "3*x1 + 10*x4 + 15*x5 >= 38",
    "3*x1 + 4*x3 + 10*x4 >= 38",
    "3*x1 + 4*x3 + 15*x5 >= 38",
    "3*x1 + 14*x2 + 4*x3 >= 38",
    "2*x0 + 3*x1 + 4*x3 >= 38",
    "2*x0 + 3*x1 + 14*x2 >= 38",
    "2*x0 + 10*x4 + 15*x5 >= 38",
    "4*x3 + 10*x4 + 15*x5 >= 38",
    "2*x0 + 14*x2 + 10*x4 >= 38",
    "14*x2 + 10*x4 + 15*x5 >= 38",
    "2*x0 + 4*x3 + 15*x5 >= 34",
    "2*x0 + 4*x3 + 10*x4 >= 34",
    "14*x2 + 4*x3 + 10*x4 >= 34",
    "3*x1 + 14*x2 + 15*x5 >= 34",
    "3*x1 + 14*x2 + 10*x4 >= 34",
    "2*x0 + 3*x1 + 15*x5 >= 34",
    "2*x0 + 14*x2 + 15*x5 >= 34",
    "3*x1 + 10*x4 + 15*x5 >= 34",
    "3*x1 + 4*x3 + 10*x4 >= 34",
    "3*x1 + 4*x3 + 15*x5 >= 34",
    "3*x1 + 14*x2 + 4*x3 >= 34",
    "2*x0 + 3*x1 + 4*x3 >= 34",
    "2*x0 + 3*x1 + 14*x2 >= 34",
    "2*x0 + 10*x4 + 15*x5 >= 34",
    "4*x3 + 10*x4 + 15*x5 >= 34",
    "2*x0 + 14*x2 + 10*x4 >= 34",
    "14*x2 + 10*x4 + 15*x5 >= 34",
    "2*x0 + 4*x3 + 15*x5 >= 29",
    "2*x0 + 4*x3 + 10*x4 >= 29",
    "14*x2 + 4*x3 + 10*x4 >= 29",
    "3*x1 + 14*x2 + 15*x5 >= 29",
    "3*x1 + 14*x2 + 10*x4 >= 29",
    "2*x0 + 3*x1 + 15*x5 >= 29",
    "2*x0 + 14*x2 + 15*x5 >= 29",
    "3*x1 + 10*x4 + 15*x5 >= 29",
    "3*x1 + 4*x3 + 10*x4 >= 29",
    "3*x1 + 4*x3 + 15*x5 >= 29",
    "3*x1 + 14*x2 + 4*x3 >= 29",
    "2*x0 + 3*x1 + 4*x3 >= 29",
    "2*x0 + 3*x1 + 14*x2 >= 29",
    "2*x0 + 10*x4 + 15*x5 >= 29",
    "4*x3 + 10*x4 + 15*x5 >= 29",
    "2*x0 + 14*x2 + 10*x4 >= 29",
    "14*x2 + 10*x4 + 15*x5 >= 29",
    "2*x0 + 4*x3 + 15*x5 >= 38",
    "2*x0 + 4*x3 + 10*x4 >= 38",
    "14*x2 + 4*x3 + 10*x4 >= 38",
    "3*x1 + 14*x2 + 15*x5 >= 38",
    "3*x1 + 14*x2 + 10*x4 >= 38",
    "2*x0 + 3*x1 + 15*x5 >= 38",
    "2*x0 + 14*x2 + 15*x5 >= 38",
    "3*x1 + 10*x4 + 15*x5 >= 38",
    "3*x1 + 4*x3 + 10*x4 >= 38",
    "3*x1 + 4*x3 + 15*x5 >= 38",
    "3*x1 + 14*x2 + 4*x3 >= 38",
    "2*x0 + 3*x1 + 4*x3 >= 38",
    "2*x0 + 3*x1 + 14*x2 >= 38",
    "2*x0 + 10*x4 + 15*x5 >= 38",
    "4*x3 + 10*x4 + 15*x5 >= 38",
    "2*x0 + 14*x2 + 10*x4 >= 38",
    "14*x2 + 10*x4 + 15*x5 >= 38",
    "2*x0 + 4*x3 + 15*x5 >= 42",
    "2*x0 + 4*x3 + 10*x4 >= 42",
    "14*x2 + 4*x3 + 10*x4 >= 42",
    "3*x1 + 14*x2 + 15*x5 >= 42",
    "3*x1 + 14*x2 + 10*x4 >= 42",
    "2*x0 + 3*x1 + 15*x5 >= 42",
    "2*x0 + 14*x2 + 15*x5 >= 42",
    "3*x1 + 10*x4 + 15*x5 >= 42",
    "3*x1 + 4*x3 + 10*x4 >= 42",
    "3*x1 + 4*x3 + 15*x5 >= 42",
    "3*x1 + 14*x2 + 4*x3 >= 42",
    "2*x0 + 3*x1 + 4*x3 >= 42",
    "2*x0 + 3*x1 + 14*x2 >= 42",
    "2*x0 + 10*x4 + 15*x5 >= 42",
    "4*x3 + 10*x4 + 15*x5 >= 42",
    "2*x0 + 14*x2 + 10*x4 >= 42",
    "14*x2 + 10*x4 + 15*x5 >= 42",
    "2*x0 + 4*x3 + 15*x5 >= 38",
    "2*x0 + 4*x3 + 10*x4 >= 38",
    "14*x2 + 4*x3 + 10*x4 >= 38",
    "3*x1 + 14*x2 + 15*x5 >= 38",
    "3*x1 + 14*x2 + 10*x4 >= 38",
    "2*x0 + 3*x1 + 15*x5 >= 38",
    "2*x0 + 14*x2 + 15*x5 >= 38",
    "3*x1 + 10*x4 + 15*x5 >= 38",
    "3*x1 + 4*x3 + 10*x4 >= 38",
    "3*x1 + 4*x3 + 15*x5 >= 38",
    "3*x1 + 14*x2 + 4*x3 >= 38",
    "2*x0 + 3*x1 + 4*x3 >= 38",
    "2*x0 + 3*x1 + 14*x2 >= 38",
    "2*x0 + 10*x4 + 15*x5 >= 38",
    "4*x3 + 10*x4 + 15*x5 >= 38",
    "2*x0 + 14*x2 + 10*x4 >= 38",
    "14*x2 + 10*x4 + 15*x5 >= 38",
    "2*x0 + 4*x3 + 15*x5 >= 33",
    "2*x0 + 4*x3 + 10*x4 >= 33",
    "14*x2 + 4*x3 + 10*x4 >= 33",
    "3*x1 + 14*x2 + 15*x5 >= 33",
    "3*x1 + 14*x2 + 10*x4 >= 33",
    "2*x0 + 3*x1 + 15*x5 >= 33",
    "2*x0 + 14*x2 + 15*x5 >= 33",
    "3*x1 + 10*x4 + 15*x5 >= 33",
    "3*x1 + 4*x3 + 10*x4 >= 33",
    "3*x1 + 4*x3 + 15*x5 >= 33",
    "3*x1 + 14*x2 + 4*x3 >= 33",
    "2*x0 + 3*x1 + 4*x3 >= 33",
    "2*x0 +