```json
{
  "sym_variables": [
    ("x0", "hours worked by Paul"),
    ("x1", "hours worked by Ringo"),
    ("x2", "hours worked by Dale"),
    ("x3", "hours worked by Hank"),
    ("x4", "hours worked by Bill"),
    ("x5", "hours worked by Jean"),
    ("x6", "hours worked by Peggy")
  ],
  "objective_function": "6.63 * x0 + 6.54 * x1 + 2.03 * x2 + 9.2 * x3 + 8.24 * x4 + 9.16 * x5 + 7.76 * x6",
  "constraints": [
    "3 * x1 + 10 * x3 >= 36",
    "2 * x5 + 22 * x6 >= 83",
    "3 * x1 + 7 * x4 >= 40",
    "1 * x0 + 7 * x4 >= 100",
    "1 * x0 + 3 * x1 + 10 * x3 >= 83",
    "3 * x1 + 5 * x2 + 10 * x3 >= 83",
    "1 * x0 + 3 * x1 + 10 * x3 >= 53",
    "3 * x1 + 5 * x2 + 10 * x3 >= 53",
    "1 * x0 + 3 * x1 + 5 * x2 + 10 * x3 + 7 * x4 + 2 * x5 + 22 * x6 >= 53",
    "3 * x2 + 6 * x4 >= 28",
    "15 * x3 + 1 * x5 >= 35",
    "6 * x4 + 1 * x6 >= 22",
    "20 * x1 + 1 * x5 >= 22",
    "20 * x1 + 3 * x2 >= 30",
    "15 * x3 + 1 * x6 >= 26",
    "21 * x0 + 1 * x5 >= 32",
    "1 * x5 + 1 * x6 >= 22",
    "20 * x1 + 15 * x3 >= 38",
    "20 * x1 + 6 * x4 >= 15",
    "3 * x2 + 15 * x3 >= 37",
    "20 * x1 + 3 * x2 + 15 * x3 >= 30",
    "21 * x0 + 20 * x1 + 6 * x4 >= 30",
    "21 * x0 + 3 * x2 + 1 * x5 >= 30",
    "20 * x1 + 6 * x4 + 1 * x6 >= 30",
    "21 * x0 + 3 * x2 + 1 * x6 >= 30",
    "21 * x0 + 15 * x3 + 1 * x6 >= 30",
    "21 * x0 + 20 * x1 + 15 * x3 >= 30",
    "20 * x1 + 3 * x2 + 1 * x5 >= 30",
    "3 * x2 + 1 * x5 + 1 * x6 >= 30",
    "3 * x2 + 15 * x3 + 1 * x6 >= 30",
    "21 * x0 + 1 * x5 + 1 * x6 >= 30",
    "3 * x2 + 15 * x3 + 6 * x4 >= 30",
    "15 * x3 + 6 * x4 + 1 * x6 >= 30",
    "3 * x2 + 6 * x4 + 1 * x6 >= 30",
    "21 * x0 + 15 * x3 + 1 * x5 >= 30",
    "6 * x4 + 1 * x5 + 1 * x6 >= 30",
    "21 * x0 + 20 * x1 + 1 * x6 >= 30",
    "3 * x2 + 15 * x3 + 1 * x5 >= 30",
    "21 * x0 + 20 * x1 + 3 * x2 >= 30",
    "20 * x1 + 3 * x2 + 6 * x4 >= 30",
    "20 * x1 + 3 * x2 + 15 * x3 >= 36",
    "21 * x0 + 20 * x1 + 6 * x4 >= 36",
    "21 * x0 + 3 * x2 + 1 * x5 >= 36",
    "20 * x1 + 6 * x4 + 1 * x6 >= 36",
    "21 * x0 + 3 * x2 + 1 * x6 >= 36",
    "21 * x0 + 15 * x3 + 1 * x6 >= 36",
    "21 * x0 + 20 * x1 + 15 * x3 >= 36",
    "20 * x1 + 3 * x2 + 1 * x5 >= 36",
    "3 * x2 + 1 * x5 + 1 * x6 >= 36",
    "3 * x2 + 15 * x3 + 1 * x6 >= 36",
    "21 * x0 + 1 * x5 + 1 * x6 >= 36",
    "3 * x2 + 15 * x3 + 6 * x4 >= 36",
    "15 * x3 + 6 * x4 + 1 * x6 >= 36",
    "3 * x2 + 6 * x4 + 1 * x6 >= 36",
    "21 * x0 + 15 * x3 + 1 * x5 >= 36",
    "6 * x4 + 1 * x5 + 1 * x6 >= 36",
    "21 * x0 + 20 * x1 + 1 * x6 >= 36",
    "3 * x2 + 15 * x3 + 1 * x5 >= 36",
    "21 * x0 + 20 * x1 + 3 * x2 >= 36",
    "20 * x1 + 3 * x2 + 6 * x4 >= 36",
    "20 * x1 + 3 * x2 + 15 * x3 >= 33",
    "21 * x0 + 20 * x1 + 6 * x4 >= 33",
    "21 * x0 + 3 * x2 + 1 * x5 >= 33",
    "20 * x1 + 6 * x4 + 1 * x6 >= 33",
    "21 * x0 + 3 * x2 + 1 * x6 >= 33",
    "21 * x0 + 15 * x3 + 1 * x6 >= 33",
    "21 * x0 + 20 * x1 + 15 * x3 >= 33",
    "20 * x1 + 3 * x2 + 1 * x5 >= 33",
    "3 * x2 + 1 * x5 + 1 * x6 >= 33",
    "3 * x2 + 15 * x3 + 1 * x6 >= 33",
    "21 * x0 + 1 * x5 + 1 * x6 >= 33",
    "3 * x2 + 15 * x3 + 6 * x4 >= 33",
    "15 * x3 + 6 * x4 + 1 * x6 >= 33",
    "3 * x2 + 6 * x4 + 1 * x6 >= 33",
    "21 * x0 + 15 * x3 + 1 * x5 >= 33",
    "6 * x4 + 1 * x5 + 1 * x6 >= 33",
    "21 * x0 + 20 * x1 + 1 * x6 >= 33",
    "3 * x2 + 15 * x3 + 1 * x5 >= 33",
    "21 * x0 + 20 * x1 + 3 * x2 >= 33",
    "20 * x1 + 3 * x2 + 6 * x4 >= 33",
    "20 * x1 + 3 * x2 + 15 * x3 >= 31",
    "21 * x0 + 20 * x1 + 6 * x4 >= 31",
    "21 * x0 + 3 * x2 + 1 * x5 >= 31",
    "20 * x1 + 6 * x4 + 1 * x6 >= 31",
    "21 * x0 + 3 * x2 + 1 * x6 >= 31",
    "21 * x0 + 15 * x3 + 1 * x6 >= 31",
    "21 * x0 + 20 * x1 + 15 * x3 >= 31",
    "20 * x1 + 3 * x2 + 1 * x5 >= 31",
    "3 * x2 + 1 * x5 + 1 * x6 >= 31",
    "3 * x2 + 15 * x3 + 1 * x6 >= 31",
    "21 * x0 + 1 * x5 + 1 * x6 >= 31",
    "3 * x2 + 15 * x3 + 6 * x4 >= 31",
    "15 * x3 + 6 * x4 + 1 * x6 >= 31",
    "3 * x2 + 6 * x4 + 1 * x6 >= 31",
    "21 * x0 + 15 * x3 + 1 * x5 >= 31",
    "6 * x4 + 1 * x5 + 1 * x6 >= 31",
    "21 * x0 + 20 * x1 + 1 * x6 >= 31",
    "3 * x2 + 15 * x3 + 1 * x5 >= 31",
    "21 * x0 + 20 * x1 + 3 * x2 >= 31",
    "20 * x1 + 3 * x2 + 6 * x4 >= 31",
    "20 * x1 + 3 * x2 + 15 * x3 >= 34",
    "21 * x0 + 20 * x1 + 6 * x4 >= 34",
    "21 * x0 + 3 * x2 + 1 * x5 >= 34",
    "20 * x1 + 6 * x4 + 1 * x6 >= 34",
    "21 * x0 + 3 * x2 + 1 * x6 >= 34",
    "21 * x0 + 15 * x3 + 1 * x6 >= 34",
    "21 * x0 + 20 * x1 + 15 * x3 >= 34",
    "20 * x1 + 3 * x2 + 1 * x5 >= 34",
    "3 * x2 + 1 * x5 + 1 * x6 >= 34",
    "3 * x2 + 15 * x3 + 1 * x6 >= 34",
    "21 * x0 + 1 * x5 + 1 * x6 >= 34",
    "3 * x2 + 15 * x3 + 6 * x4 >= 34",
    "15 * x3 + 6 * x4 + 1 * x6 >= 34",
    "3 * x2 + 6 * x4 + 1 * x6 >= 34",
    "21 * x0 + 15 * x3 + 1 * x5 >= 34",
    "6 * x4 + 1 * x5 + 1 * x6 >= 34",
    "21 * x0 + 20 * x1 + 1 * x6 >= 34",
    "3 * x2 + 15 * x3 + 1 * x5 >= 34",
    "21 * x0 + 20 * x1 + 3 * x2 >= 34",
    "20 * x1 + 3 * x2 + 6 * x4 >= 34",
    "20 * x1 + 3 * x2 + 15 * x3 >= 25",
    "21 * x0 + 20 * x1 + 6 * x4 >= 25",
    "21 * x0 + 3 * x2 + 1 * x5 >= 25",
    "20 * x1 + 6 * x4 + 1 * x6 >= 25",
    "21 * x0 + 3 * x2 + 1 * x6 >= 25",
    "21 * x0 + 15 * x3 + 1 * x6 >= 25",
    "21 * x0 + 20 * x1 + 15 * x3 >= 25",
    "20 * x1 + 3 * x2 + 1 * x5 >= 25",
    "3 * x2 + 1 * x5 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 1 * x6 >= 25",
    "21 * x0 + 1 * x5 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 6 * x4 >= 25",
    "15 * x3 + 6 * x4 + 1 * x6 >= 25",
    "3 * x2 + 6 * x4 + 1 * x6 >= 25",
    "21 * x0 + 15 * x3 + 1 * x5 >= 25",
    "6 * x4 + 1 * x5 + 1 * x6 >= 25",
    "21 * x0 + 20 * x1 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 1 * x5 >= 25",
    "21 * x0 + 20 * x1 + 3 * x2 >= 25",
    "20 * x1 + 3 * x2 + 6 * x4 >= 25",
    "20 * x1 + 3 * x2 + 15 * x3 >= 34",
    "21 * x0 + 20 * x1 + 6 * x4 >= 34",
    "21 * x0 + 3 * x2 + 1 * x5 >= 34",
    "20 * x1 + 6 * x4 + 1 * x6 >= 34",
    "21 * x0 + 3 * x2 + 1 * x6 >= 34",
    "21 * x0 + 15 * x3 + 1 * x6 >= 34",
    "21 * x0 + 20 * x1 + 15 * x3 >= 34",
    "20 * x1 + 3 * x2 + 1 * x5 >= 34",
    "3 * x2 + 1 * x5 + 1 * x6 >= 34",
    "3 * x2 + 15 * x3 + 1 * x6 >= 34",
    "21 * x0 + 1 * x5 + 1 * x6 >= 34",
    "3 * x2 + 15 * x3 + 6 * x4 >= 34",
    "15 * x3 + 6 * x4 + 1 * x6 >= 34",
    "3 * x2 + 6 * x4 + 1 * x6 >= 34",
    "21 * x0 + 15 * x3 + 1 * x5 >= 34",
    "6 * x4 + 1 * x5 + 1 * x6 >= 34",
    "21 * x0 + 20 * x1 + 1 * x6 >= 34",
    "3 * x2 + 15 * x3 + 1 * x5 >= 34",
    "21 * x0 + 20 * x1 + 3 * x2 >= 34",
    "20 * x1 + 3 * x2 + 6 * x4 >= 34",
    "20 * x1 + 3 * x2 + 15 * x3 >= 28",
    "21 * x0 + 20 * x1 + 6 * x4 >= 28",
    "21 * x0 + 3 * x2 + 1 * x5 >= 28",
    "20 * x1 + 6 * x4 + 1 * x6 >= 28",
    "21 * x0 + 3 * x2 + 1 * x6 >= 28",
    "21 * x0 + 15 * x3 + 1 * x6 >= 28",
    "21 * x0 + 20 * x1 + 15 * x3 >= 28",
    "20 * x1 + 3 * x2 + 1 * x5 >= 28",
    "3 * x2 + 1 * x5 + 1 * x6 >= 28",
    "3 * x2 + 15 * x3 + 1 * x6 >= 28",
    "21 * x0 + 1 * x5 + 1 * x6 >= 28",
    "3 * x2 + 15 * x3 + 6 * x4 >= 28",
    "15 * x3 + 6 * x4 + 1 * x6 >= 28",
    "3 * x2 + 6 * x4 + 1 * x6 >= 28",
    "21 * x0 + 15 * x3 + 1 * x5 >= 28",
    "6 * x4 + 1 * x5 + 1 * x6 >= 28",
    "21 * x0 + 20 * x1 + 1 * x6 >= 28",
    "3 * x2 + 15 * x3 + 1 * x5 >= 28",
    "21 * x0 + 20 * x1 + 3 * x2 >= 28",
    "20 * x1 + 3 * x2 + 6 * x4 >= 28",
    "20 * x1 + 3 * x2 + 15 * x3 >= 25",
    "21 * x0 + 20 * x1 + 6 * x4 >= 25",
    "21 * x0 + 3 * x2 + 1 * x5 >= 25",
    "20 * x1 + 6 * x4 + 1 * x6 >= 25",
    "21 * x0 + 3 * x2 + 1 * x6 >= 25",
    "21 * x0 + 15 * x3 + 1 * x6 >= 25",
    "21 * x0 + 20 * x1 + 15 * x3 >= 25",
    "20 * x1 + 3 * x2 + 1 * x5 >= 25",
    "3 * x2 + 1 * x5 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 1 * x6 >= 25",
    "21 * x0 + 1 * x5 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 6 * x4 >= 25",
    "15 * x3 + 6 * x4 + 1 * x6 >= 25",
    "3 * x2 + 6 * x4 + 1 * x6 >= 25",
    "21 * x0 + 15 * x3 + 1 * x5 >= 25",
    "6 * x4 + 1 * x5 + 1 * x6 >= 25",
    "21 * x0 + 20 * x1 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 1 * x5 >= 25",
    "21 * x0 + 20 * x1 + 3 * x2 >= 25",
    "20 * x1 + 3 * x2 + 6 * x4 >= 25",
    "20 * x1 + 3 * x2 + 15 * x3 >= 35",
    "21 * x0 + 20 * x1 + 6 * x4 >= 35",
    "21 * x0 + 3 * x2 + 1 * x5 >= 35",
    "20 * x1 + 6 * x4 + 1 * x6 >= 35",
    "21 * x0 + 3 * x2 + 1 * x6 >= 35",
    "21 * x0 + 15 * x3 + 1 * x6 >= 35",
    "21 * x0 + 20 * x1 + 15 * x3 >= 35",
    "20 * x1 + 3 * x2 + 1 * x5 >= 35",
    "3 * x2 + 1 * x5 + 1 * x6 >= 35",
    "3 * x2 + 15 * x3 + 1 * x6 >= 35",
    "21 * x0 + 1 * x5 + 1 * x6 >= 35",
    "3 * x2 + 15 * x3 + 6 * x4 >= 35",
    "15 * x3 + 6 * x4 + 1 * x6 >= 35",
    "3 * x2 + 6 * x4 + 1 * x6 >= 35",
    "21 * x0 + 15 * x3 + 1 * x5 >= 35",
    "6 * x4 + 1 * x5 + 1 * x6 >= 35",
    "21 * x0 + 20 * x1 + 1 * x6 >= 35",
    "3 * x2 + 15 * x3 + 1 * x5 >= 35",
    "21 * x0 + 20 * x1 + 3 * x2 >= 35",
    "20 * x1 + 3 * x2 + 6 * x4 >= 35",
    "20 * x1 + 3 * x2 + 15 * x3 >= 25",
    "21 * x0 + 20 * x1 + 6 * x4 >= 25",
    "21 * x0 + 3 * x2 + 1 * x5 >= 25",
    "20 * x1 + 6 * x4 + 1 * x6 >= 25",
    "21 * x0 + 3 * x2 + 1 * x6 >= 25",
    "21 * x0 + 15 * x3 + 1 * x6 >= 25",
    "21 * x0 + 20 * x1 + 15 * x3 >= 25",
    "20 * x1 + 3 * x2 + 1 * x5 >= 25",
    "3 * x2 + 1 * x5 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 1 * x6 >= 25",
    "21 * x0 + 1 * x5 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 6 * x4 >= 25",
    "15 * x3 + 6 * x4 + 1 * x6 >= 25",
    "3 * x2 + 6 * x4 + 1 * x6 >= 25",
    "21 * x0 + 15 * x3 + 1 * x5 >= 25",
    "6 * x4 + 1 * x5 + 1 * x6 >= 25",
    "21 * x0 + 20 * x1 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 1 * x5 >= 25",
    "21 * x0 + 20 * x1 + 3 * x2 >= 25",
    "20 * x1 + 3 * x2 + 6 * x4 >= 25",
    "20 * x1 + 3 * x2 + 15 * x3 >= 28",
    "21 * x0 + 20 * x1 + 6 * x4 >= 28",
    "21 * x0 + 3 * x2 + 1 * x5 >= 28",
    "20 * x1 + 6 * x4 + 1 * x6 >= 28",
    "21 * x0 + 3 * x2 + 1 * x6 >= 28",
    "21 * x0 + 15 * x3 + 1 * x6 >= 28",
    "21 * x0 + 20 * x1 + 15 * x3 >= 28",
    "20 * x1 + 3 * x2 + 1 * x5 >= 28",
    "3 * x2 + 1 * x5 + 1 * x6 >= 28",
    "3 * x2 + 15 * x3 + 1 * x6 >= 28",
    "21 * x0 + 1 * x5 + 1 * x6 >= 28",
    "3 * x2 + 15 * x3 + 6 * x4 >= 28",
    "15 * x3 + 6 * x4 + 1 * x6 >= 28",
    "3 * x2 + 6 * x4 + 1 * x6 >= 28",
    "21 * x0 + 15 * x3 + 1 * x5 >= 28",
    "6 * x4 + 1 * x5 + 1 * x6 >= 28",
    "21 * x0 + 20 * x1 + 1 * x6 >= 28",
    "3 * x2 + 15 * x3 + 1 * x5 >= 28",
    "21 * x0 + 20 * x1 + 3 * x2 >= 28",
    "20 * x1 + 3 * x2 + 6 * x4 >= 28",
    "20 * x1 + 3 * x2 + 15 * x3 >= 25",
    "21 * x0 + 20 * x1 + 6 * x4 >= 25",
    "21 * x0 + 3 * x2 + 1 * x5 >= 25",
    "20 * x1 + 6 * x4 + 1 * x6 >= 25",
    "21 * x0 + 3 * x2 + 1 * x6 >= 25",
    "21 * x0 + 15 * x3 + 1 * x6 >= 25",
    "21 * x0 + 20 * x1 + 15 * x3 >= 25",
    "20 * x1 + 3 * x2 + 1 * x5 >= 25",
    "3 * x2 + 1 * x5 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 1 * x6 >= 25",
    "21 * x0 + 1 * x5 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 6 * x4 >= 25",
    "15 * x3 + 6 * x4 + 1 * x6 >= 25",
    "3 * x2 + 6 * x4 + 1 * x6 >= 25",
    "21 * x0 + 15 * x3 + 1 * x5 >= 25",
    "6 * x4 + 1 * x5 + 1 * x6 >= 25",
    "21 * x0 + 20 * x1 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 1 * x5 >= 25",
    "21 * x0 + 20 * x1 + 3 * x2 >= 25",
    "20 * x1 + 3 * x2 + 6 * x4 >= 25",
    "20 * x1 + 3 * x2 + 15 * x3 >= 28",
    "21 * x0 + 20 * x1 + 6 * x4 >= 28",
    "21 * x0 + 3 * x2 + 1 * x5 >= 28",
    "20 * x1 + 6 * x4 + 1 * x6 >= 28",
    "21 * x0 + 3 * x2 + 1 * x6 >= 28",
    "21 * x0 + 15 * x3 + 1 * x6 >= 28",
    "21 * x0 + 20 * x1 + 15 * x3 >= 28",
    "20 * x1 + 3 * x2 + 1 * x5 >= 28",
    "3 * x2 + 1 * x5 + 1 * x6 >= 28",
    "3 * x2 + 15 * x3 + 1 * x6 >= 28",
    "21 * x0 + 1 * x5 + 1 * x6 >= 28",
    "3 * x2 + 15 * x3 + 6 * x4 >= 28",
    "15 * x3 + 6 * x4 + 1 * x6 >= 28",
    "3 * x2 + 6 * x4 + 1 * x6 >= 28",
    "21 * x0 + 15 * x3 + 1 * x5 >= 28",
    "6 * x4 + 1 * x5 + 1 * x6 >= 28",
    "21 * x0 + 20 * x1 + 1 * x6 >= 28",
    "3 * x2 + 15 * x3 + 1 * x5 >= 28",
    "21 * x0 + 20 * x1 + 3 * x2 >= 28",
    "20 * x1 + 3 * x2 + 6 * x4 >= 28",
    "20 * x1 + 3 * x2 + 15 * x3 >= 25",
    "21 * x0 + 20 * x1 + 6 * x4 >= 25",
    "21 * x0 + 3 * x2 + 1 * x5 >= 25",
    "20 * x1 + 6 * x4 + 1 * x6 >= 25",
    "21 * x0 + 3 * x2 + 1 * x6 >= 25",
    "21 * x0 + 15 * x3 + 1 * x6 >= 25",
    "21 * x0 + 20 * x1 + 15 * x3 >= 25",
    "20 * x1 + 3 * x2 + 1 * x5 >= 25",
    "3 * x2 + 1 * x5 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 1 * x6 >= 25",
    "21 * x0 + 1 * x5 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 6 * x4 >= 25",
    "15 * x3 + 6 * x4 + 1 * x6 >= 25",
    "3 * x2 + 6 * x4 + 1 * x6 >= 25",
    "21 * x0 + 15 * x3 + 1 * x5 >= 25",
    "6 * x4 + 1 * x5 + 1 * x6 >= 25",
    "21 * x0 + 20 * x1 + 1 * x6 >= 25",
    "3 * x2 + 15 * x3 + 1 * x5 >= 25",
    "21 * x0 + 20 * x1 + 3 * x2 >= 25",
    "20 * x1 + 3 * x2 + 6 * x4 >= 25",
    "20 * x1 + 3