```json
{
  "sym_variables": [
    ("x0", "hours worked by Peggy"),
    ("x1", "hours worked by John"),
    ("x2", "hours worked by Dale"),
    ("x3", "hours worked by Laura"),
    ("x4", "hours worked by Bill"),
    ("x5", "hours worked by Ringo"),
    ("x6", "hours worked by George")
  ],
  "objective_function": "2.61*x0 + 5.96*x1 + 2.97*x2 + 9.77*x3 + 8.75*x4 + 2.62*x5 + 4.41*x6",
  "constraints": [
    "1.01*x2 + 1.18*x4 >= 8",
    "1.18*x4 + 1.6*x5 >= 12",
    "1.18*x4 + 0.8*x6 >= 19",
    "1.01*x2 + 1.6*x5 >= 8",
    "1.6*x5 + 0.8*x6 >= 8",
    "1.27*x1 + 1.01*x2 >= 18",
    "2.69*x0 + 1.6*x5 >= 11",
    "2.69*x0 + 0.8*x6 >= 20",
    "2.69*x0 + 1.18*x4 >= 7",
    "1.01*x2 + 0.8*x6 >= 12",
    "1.27*x1 + 0.8*x6 >= 14",
    "1.01*x2 + 1.6*x5 + 0.8*x6 >= 13",
    "1.01*x2 + 0.9*x3 + 1.18*x4 >= 13",
    "1.27*x1 + 0.9*x3 + 1.18*x4 >= 13",
    "1.27*x1 + 1.6*x5 + 0.8*x6 >= 13",
    "1.27*x1 + 1.01*x2 + 1.6*x5 >= 13",
    "2.69*x0 + 1.27*x1 + 0.8*x6 >= 13",
    "1.27*x1 + 1.18*x4 + 0.8*x6 >= 13",
    "1.01*x2 + 1.18*x4 + 0.8*x6 >= 13",
    "1.27*x1 + 0.9*x3 + 1.6*x5 >= 13",
    "2.69*x0 + 1.18*x4 + 1.6*x5 >= 13",
    "1.27*x1 + 1.01*x2 + 1.18*x4 >= 13",
    "2.69*x0 + 0.9*x3 + 0.8*x6 >= 13",
    "1.01*x2 + 0.9*x3 + 1.6*x5 >= 13",
    "2.69*x0 + 0.9*x3 + 1.18*x4 >= 13",
    "2.69*x0 + 1.6*x5 + 0.8*x6 >= 13",
    "0.9*x3 + 1.18*x4 + 0.8*x6 >= 13",
    "1.27*x1 + 1.01*x2 + 0.8*x6 >= 13",
    "2.69*x0 + 1.01*x2 + 0.9*x3 >= 13",
    "2.69*x0 + 1.27*x1 + 1.6*x5 >= 13",
    "2.69*x0 + 1.18*x4 + 0.8*x6 >= 13",
    "0.9*x3 + 1.6*x5 + 0.8*x6 >= 13",
    "2.69*x0 + 1.27*x1 + 1.18*x4 >= 13",
    "2.69*x0 + 1.01*x2 + 1.18*x4 >= 13",
    "1.01*x2 + 1.6*x5 + 0.8*x6 >= 19",
    "1.01*x2 + 0.9*x3 + 1.18*x4 >= 19",
    "1.27*x1 + 0.9*x3 + 1.18*x4 >= 19",
    "1.27*x1 + 1.6*x5 + 0.8*x6 >= 19",
    "1.27*x1 + 1.01*x2 + 1.6*x5 >= 19",
    "2.69*x0 + 1.27*x1 + 0.8*x6 >= 19",
    "1.27*x1 + 1.18*x4 + 0.8*x6 >= 19",
    "1.01*x2 + 1.18*x4 + 0.8*x6 >= 19",
    "1.27*x1 + 0.9*x3 + 1.6*x5 >= 19",
    "2.69*x0 + 1.18*x4 + 1.6*x5 >= 19",
    "1.27*x1 + 1.01*x2 + 1.18*x4 >= 19",
    "2.69*x0 + 0.9*x3 + 0.8*x6 >= 19",
    "1.01*x2 + 0.9*x3 + 1.6*x5 >= 19",
    "2.69*x0 + 0.9*x3 + 1.18*x4 >= 19",
    "2.69*x0 + 1.6*x5 + 0.8*x6 >= 19",
    "0.9*x3 + 1.18*x4 + 0.8*x6 >= 19",
    "1.27*x1 + 1.01*x2 + 0.8*x6 >= 19",
    "2.69*x0 + 1.01*x2 + 0.9*x3 >= 19",
    "2.69*x0 + 1.27*x1 + 1.6*x5 >= 19",
    "2.69*x0 + 1.18*x4 + 0.8*x6 >= 19",
    "0.9*x3 + 1.6*x5 + 0.8*x6 >= 19",
    "2.69*x0 + 1.27*x1 + 1.18*x4 >= 19",
    "2.69*x0 + 1.01*x2 + 1.18*x4 >= 19",
    "1.01*x2 + 1.6*x5 + 0.8*x6 >= 17",
    "1.01*x2 + 0.9*x3 + 1.18*x4 >= 17",
    "1.27*x1 + 0.9*x3 + 1.18*x4 >= 17",
    "1.27*x1 + 1.6*x5 + 0.8*x6 >= 17",
    "1.27*x1 + 1.01*x2 + 1.6*x5 >= 17",
    "2.69*x0 + 1.27*x1 + 0.8*x6 >= 17",
    "1.27*x1 + 1.18*x4 + 0.8*x6 >= 17",
    "1.01*x2 + 1.18*x4 + 0.8*x6 >= 17",
    "1.27*x1 + 0.9*x3 + 1.6*x5 >= 17",
    "2.69*x0 + 1.18*x4 + 1.6*x5 >= 17",
    "1.27*x1 + 1.01*x2 + 1.18*x4 >= 17",
    "2.69*x0 + 0.9*x3 + 0.8*x6 >= 17",
    "1.01*x2 + 0.9*x3 + 1.6*x5 >= 17",
    "2.69*x0 + 0.9*x3 + 1.18*x4 >= 17",
    "2.69*x0 + 1.6*x5 + 0.8*x6 >= 17",
    "0.9*x3 + 1.18*x4 + 0.8*x6 >= 17",
    "1.27*x1 + 1.01*x2 + 0.8*x6 >= 17",
    "2.69*x0 + 1.01*x2 + 0.9*x3 >= 17",
    "2.69*x0 + 1.27*x1 + 1.6*x5 >= 17",
    "2.69*x0 + 1.18*x4 + 0.8*x6 >= 17",
    "0.9*x3 + 1.6*x5 + 0.8*x6 >= 17",
    "2.69*x0 + 1.27*x1 + 1.18*x4 >= 17",
    "2.69*x0 + 1.01*x2 + 1.18*x4 >= 17",
    "1.01*x2 + 1.6*x5 + 0.8*x6 >= 11",
    "1.01*x2 + 0.9*x3 + 1.18*x4 >= 11",
    "1.27*x1 + 0.9*x3 + 1.18*x4 >= 11",
    "1.27*x1 + 1.6*x5 + 0.8*x6 >= 11",
    "1.27*x1 + 1.01*x2 + 1.6*x5 >= 11",
    "2.69*x0 + 1.27*x1 + 0.8*x6 >= 11",
    "1.27*x1 + 1.18*x4 + 0.8*x6 >= 11",
    "1.01*x2 + 1.18*x4 + 0.8*x6 >= 11",
    "1.27*x1 + 0.9*x3 + 1.6*x5 >= 11",
    "2.69*x0 + 1.18*x4 + 1.6*x5 >= 11",
    "1.27*x1 + 1.01*x2 + 1.18*x4 >= 11",
    "2.69*x0 + 0.9*x3 + 0.8*x6 >= 11",
    "1.01*x2 + 0.9*x3 + 1.6*x5 >= 11",
    "2.69*x0 + 0.9*x3 + 1.18*x4 >= 11",
    "2.69*x0 + 1.6*x5 + 0.8*x6 >= 11",
    "0.9*x3 + 1.18*x4 + 0.8*x6 >= 11",
    "1.27*x1 + 1.01*x2 + 0.8*x6 >= 11",
    "2.69*x0 + 1.01*x2 + 0.9*x3 >= 11",
    "2.69*x0 + 1.27*x1 + 1.6*x5 >= 11",
    "2.69*x0 + 1.18*x4 + 0.8*x6 >= 11",
    "0.9*x3 + 1.6*x5 + 0.8*x6 >= 11",
    "2.69*x0 + 1.27*x1 + 1.18*x4 >= 11",
    "2.69*x0 + 1.01*x2 + 1.18*x4 >= 11",
    "1.01*x2 + 1.6*x5 + 0.8*x6 >= 18",
    "1.01*x2 + 0.9*x3 + 1.18*x4 >= 18",
    "1.27*x1 + 0.9*x3 + 1.18*x4 >= 18",
    "1.27*x1 + 1.6*x5 + 0.8*x6 >= 18",
    "1.27*x1 + 1.01*x2 + 1.6*x5 >= 18",
    "2.69*x0 + 1.27*x1 + 0.8*x6 >= 18",
    "1.27*x1 + 1.18*x4 + 0.8*x6 >= 18",
    "1.01*x2 + 1.18*x4 + 0.8*x6 >= 18",
    "1.27*x1 + 0.9*x3 + 1.6*x5 >= 18",
    "2.69*x0 + 1.18*x4 + 1.6*x5 >= 18",
    "1.27*x1 + 1.01*x2 + 1.18*x4 >= 18",
    "2.69*x0 + 0.9*x3 + 0.8*x6 >= 18",
    "1.01*x2 + 0.9*x3 + 1.6*x5 >= 18",
    "2.69*x0 + 0.9*x3 + 1.18*x4 >= 18",
    "2.69*x0 + 1.6*x5 + 0.8*x6 >= 18",
    "0.9*x3 + 1.18*x4 + 0.8*x6 >= 18",
    "1.27*x1 + 1.01*x2 + 0.8*x6 >= 18",
    "2.69*x0 + 1.01*x2 + 0.9*x3 >= 18",
    "2.69*x0 + 1.27*x1 + 1.6*x5 >= 18",
    "2.69*x0 + 1.18*x4 + 0.8*x6 >= 18",
    "0.9*x3 + 1.6*x5 + 0.8*x6 >= 18",
    "2.69*x0 + 1.27*x1 + 1.18*x4 >= 18",
    "2.69*x0 + 1.01*x2 + 1.18*x4 >= 18",
    "1.01*x2 + 1.6*x5 + 0.8*x6 >= 12",
    "1.01*x2 + 0.9*x3 + 1.18*x4 >= 12",
    "1.27*x1 + 0.9*x3 + 1.18*x4 >= 12",
    "1.27*x1 + 1.6*x5 + 0.8*x6 >= 12",
    "1.27*x1 + 1.01*x2 + 1.6*x5 >= 12",
    "2.69*x0 + 1.27*x1 + 0.8*x6 >= 12",
    "1.27*x1 + 1.18*x4 + 0.8*x6 >= 12",
    "1.01*x2 + 1.18*x4 + 0.8*x6 >= 12",
    "1.27*x1 + 0.9*x3 + 1.6*x5 >= 12",
    "2.69*x0 + 1.18*x4 + 1.6*x5 >= 12",
    "1.27*x1 + 1.01*x2 + 1.18*x4 >= 12",
    "2.69*x0 + 0.9*x3 + 0.8*x6 >= 12",
    "1.01*x2 + 0.9*x3 + 1.6*x5 >= 12",
    "2.69*x0 + 0.9*x3 + 1.18*x4 >= 12",
    "2.69*x0 + 1.6*x5 + 0.8*x6 >= 12",
    "0.9*x3 + 1.18*x4 + 0.8*x6 >= 12",
    "1.27*x1 + 1.01*x2 + 0.8*x6 >= 12",
    "2.69*x0 + 1.01*x2 + 0.9*x3 >= 12",
    "2.69*x0 + 1.27*x1 + 1.6*x5 >= 12",
    "2.69*x0 + 1.18*x4 + 0.8*x6 >= 12",
    "0.9*x3 + 1.6*x5 + 0.8*x6 >= 12",
    "2.69*x0 + 1.27*x1 + 1.18*x4 >= 12",
    "2.69*x0 + 1.01*x2 + 1.18*x4 >= 12",
    "1.01*x2 + 1.6*x5 + 0.8*x6 >= 20",
    "1.01*x2 + 0.9*x3 + 1.18*x4 >= 20",
    "1.27*x1 + 0.9*x3 + 1.18*x4 >= 20",
    "1.27*x1 + 1.6*x5 + 0.8*x6 >= 20",
    "1.27*x1 + 1.01*x2 + 1.6*x5 >= 20",
    "2.69*x0 + 1.27*x1 + 0.8*x6 >= 20",
    "1.27*x1 + 1.18*x4 + 0.8*x6 >= 20",
    "1.01*x2 + 1.18*x4 + 0.8*x6 >= 20",
    "1.27*x1 + 0.9*x3 + 1.6*x5 >= 20",
    "2.69*x0 + 1.18*x4 + 1.6*x5 >= 20",
    "1.27*x1 + 1.01*x2 + 1.18*x4 >= 20",
    "2.69*x0 + 0.9*x3 + 0.8*x6 >= 20",
    "1.01*x2 + 0.9*x3 + 1.6*x5 >= 20",
    "2.69*x0 + 0.9*x3 + 1.18*x4 >= 20",
    "2.69*x0 + 1.6*x5 + 0.8*x6 >= 20",
    "0.9*x3 + 1.18*x4 + 0.8*x6 >= 20",
    "1.27*x1 + 1.01*x2 + 0.8*x6 >= 20",
    "2.69*x0 + 1.01*x2 + 0.9*x3 >= 20",
    "2.69*x0 + 1.27*x1 + 1.6*x5 >= 20",
    "2.69*x0 + 1.18*x4 + 0.8*x6 >= 20",
    "0.9*x3 + 1.6*x5 + 0.8*x6 >= 20",
    "2.69*x0 + 1.27*x1 + 1.18*x4 >= 20",
    "2.69*x0 + 1.01*x2 + 1.18*x4 >= 20",
    "1.01*x2 + 1.6*x5 + 0.8*x6 >= 15",
    "1.01*x2 + 0.9*x3 + 1.18*x4 >= 15",
    "1.27*x1 + 0.9*x3 + 1.18*x4 >= 15",
    "1.27*x1 + 1.6*x5 + 0.8*x6 >= 15",
    "1.27*x1 + 1.01*x2 + 1.6*x5 >= 15",
    "2.69*x0 + 1.27*x1 + 0.8*x6 >= 15",
    "1.27*x1 + 1.18*x4 + 0.8*x6 >= 15",
    "1.01*x2 + 1.18*x4 + 0.8*x6 >= 15",
    "1.27*x1 + 0.9*x3 + 1.6*x5 >= 15",
    "2.69*x0 + 1.18*x4 + 1.6*x5 >= 15",
    "1.27*x1 + 1.01*x2 + 1.18*x4 >= 15",
    "2.69*x0 + 0.9*x3 + 0.8*x6 >= 15",
    "1.01*x2 + 0.9*x3 + 1.6*x5 >= 15",
    "2.69*x0 + 0.9*x3 + 1.18*x4 >= 15",
    "2.69*x0 + 1.6*x5 + 0.8*x6 >= 15",
    "0.9*x3 + 1.18*x4 + 0.8*x6 >= 15",
    "1.27*x1 + 1.01*x2 + 0.8*x6 >= 15",
    "2.69*x0 + 1.01*x2 + 0.9*x3 >= 15",
    "2.69*x0 + 1.27*x1 + 1.6*x5 >= 15",
    "2.69*x0 + 1.18*x4 + 0.8*x6 >= 15",
    "0.9*x3 + 1.6*x5 + 0.8*x6 >= 15",
    "2.69*x0 + 1.27*x1 + 1.18*x4 >= 15",
    "2.69*x0 + 1.01*x2 + 1.18*x4 >= 15",
    "1.01*x2 + 1.6*x5 + 0.8*x6 >= 14",
    "1.01*x2 + 0.9*x3 + 1.18*x4 >= 14",
    "1.27*x1 + 0.9*x3 + 1.18*x4 >= 14",
    "1.27*x1 + 1.6*x5 + 0.8*x6 >= 14",
    "1.27*x1 + 1.01*x2 + 1.6*x5 >= 14",
    "2.69*x0 + 1.27*x1 + 0.8*x6 >= 14",
    "1.27*x1 + 1.18*x4 + 0.8*x6 >= 14",
    "1.01*x2 + 1.18*x4 + 0.8*x6 >= 14",
    "1.27*x1 + 0.9*x3 + 1.6*x5 >= 14",
    "2.69*x0 + 1.18*x4 + 1.6*x5 >= 14",
    "1.27*x1 + 1.01*x2 + 1.18*x4 >= 14",
    "2.69*x0 + 0.9*x3 + 0.8*x6 >= 14",
    "1.01*x2 + 0.9*x3 + 1.6*x5 >= 14",
    "2.69*x0 + 0.9*x3 + 1.18*x4 >= 14",
    "2.69*x0 + 1.6*x5 + 0.8*x6 >= 14",
    "0.9*x3 + 1.18*x4 + 0.8*x6 >= 14",
    "1.27*x1 + 1.01*x2 + 0.8*x6 >= 14",
    "2.69*x0 + 1.01*x2 + 0.9*x3 >= 14",
    "2.69*x0 + 1.27*x1 + 1.6*x5 >= 14",
    "2.69*x0 + 1.18*x4 + 0.8*x6 >= 14",
    "0.9*x3 + 1.6*x5 + 0.8*x6 >= 14",
    "2.69*x0 + 1.27*x1 + 1.18*x4 >= 14",
    "2.69*x0 + 1.01*x2 + 1.18*x4 >= 14",
    "1.01*x2 + 1.6*x5 + 0.8*x6 >= 10",
    "1.01*x2 + 0.9*x3 + 1.18*x4 >= 10",
    "1.27*x1 + 0.9*x3 + 1.18*x4 >= 10",
    "1.27*x1 + 1.6*x5 + 0.8*x6 >= 10",
    "1.27*x1 + 1.01*x2 + 1.6*x5 >= 10",
    "2.69*x0 + 1.27*x1 + 0.8*x6 >= 10",
    "1.27*x1 + 1.18*x4 + 0.8*x6 >= 10",
    "1.01*x2 + 1.18*x4 + 0.8*x6 >= 10",
    "1.27*x1 + 0.9*x3 + 1.6*x5 >= 10",
    "2.69*x0 + 1.18*x4 + 1.6*x5 >= 10",
    "1.27*x1 + 1.01*x2 + 1.18*x4 >= 10",
    "2.69*x0 + 0.9*x3 + 0.8*x6 >= 10",
    "1.01*x2 + 0.9*x3 + 1.6*x5 >= 10",
    "2.69*x0 + 0.9*x3 + 1.18*x4 >= 10",
    "2.69*x0 + 1.6*x5 + 0.8*x6 >= 10",
    "0.9*x3 + 1.18*x4 + 0.8*x6 >= 10",
    "1.27*x1 + 1.01*x2 + 0.8*x6 >= 10",
    "2.69*x0 + 1.01*x2 + 0.9*x3 >= 10",
    "2.69*x0 + 1.27*x1 + 1.6*x5 >= 10",
    "2.69*x0 + 1.18*x4 + 0.8*x6 >= 10",
    "0.9*x3 + 1.6*x5 + 0.8*x6 >= 10",
    "2.69*x0 + 1.27*x1 + 1.18*x4 >= 10",
    "2.69*x0 + 1.01*x2 + 1.18*x4 >= 10",
    "0.28*x0 + 1.1*x1 >= 14",
    "0.2*x2 + 0.13*x5 >= 17",
    "0.28*x0 + 0.2*x2 >= 8",
    "0.2*x2 + 0.38*x4 >= 19",
    "0.28*x0 + 1.14*x6 >= 6",
    "1.1*x1 + 0.38*x4 >= 8",
    "1.1*x1 + 0.13*x5 >= 16",
    "0.13*x5 + 1.14*x6 >= 8",
    "2.03*x3 + 0.38*x4 >= 19",
    "1.1*x1 + 0.2*x2 + 1.14*x6 >= 19",
    "0.2*x2 + 2.03*x3 + 1.14*x6 >= 19",
    "0.28*x0 + 0.13*x5 + 1.14*x6 >= 19",
    "0.2*x2 + 0.38*x4 + 0.13*x5 >= 19",
    "0.28*x0 + 0.2*x2 + 0.13*x5 >= 19",
    "0.28*x0 + 0.38*x4 + 1.14*x6 >= 19",
    "0.28*x0 + 2.03*x3 + 0.38*x4 >= 19",
    "1.1*x1 + 0.2*x2 + 2.03*x3 >= 19",
    "