```json
{
  "sym_variables": [
    ("x0", "hamburgers"),
    ("x1", "eggs"),
    ("x2", "protein bars"),
    ("x3", "pickles")
  ],
  "objective_function": "5*x0 + 1*x1 + 7*x2 + 6*x3",
  "constraints": [
    "11*x0 + 7*x1 + 7*x2 + 1*x3 <= 159",
    "8*x0 + 14*x1 + 1*x2 + 4*x3 <= 87",
    "5*x0 + 11*x1 + 10*x2 + 7*x3 <= 132",
    "7*x1 + 1*x3 >= 14",
    "7*x1 + 7*x2 >= 34",
    "11*x0 + 7*x1 >= 22",
    "1*x2 + 4*x3 >= 20",
    "14*x1 + 1*x2 >= 14",
    "8*x0 + 4*x3 >= 9",
    "14*x1 + 1*x2 + 4*x3 >= 21",
    "8*x0 + 1*x2 + 4*x3 >= 21",
    "8*x0 + 14*x1 + 1*x2 >= 21",
    "8*x0 + 14*x1 + 4*x3 >= 21",
    "14*x1 + 1*x2 + 4*x3 >= 10",
    "8*x0 + 1*x2 + 4*x3 >= 10",
    "8*x0 + 14*x1 + 1*x2 >= 10",
    "8*x0 + 14*x1 + 4*x3 >= 10",
    "14*x1 + 1*x2 + 4*x3 >= 15",
    "8*x0 + 1*x2 + 4*x3 >= 15",
    "8*x0 + 14*x1 + 1*x2 >= 15",
    "8*x0 + 14*x1 + 4*x3 >= 15",
    "11*x1 + 7*x3 >= 28",
    "5*x0 + 10*x2 >= 17",
    "5*x0 + 7*x3 >= 28",
    "11*x0 + 1*x3 <= 68",
    "7*x1 + 1*x3 <= 46",
    "11*x0 + 7*x2 + 1*x3 <= 61",
    "11*x0 + 7*x1 + 7*x2 <= 39",
    "11*x0 + 7*x1 + 7*x2 + 1*x3 <= 39",
    "14*x1 + 1*x2 <= 41",
    "8*x0 + 1*x2 <= 31",
    "1*x2 + 4*x3 <= 56",
    "8*x0 + 14*x1 <= 40",
    "8*x0 + 14*x1 + 1*x2 <= 41",
    "8*x0 + 14*x1 + 1*x2 + 4*x3 <= 41",
    "5*x0 + 11*x1 <= 55",
    "5*x0 + 10*x2 + 7*x3 <= 99",
    "5*x0 + 11*x1 + 7*x3 <= 101",
    "5*x0 + 11*x1 + 10*x2 + 7*x3 <= 101"

  ]
}
```

```python
import gurobipy as gp

# Create a new model
m = gp.Model("optimization_problem")

# Create variables
hamburgers = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="hamburgers")
eggs = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="eggs")
protein_bars = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="protein_bars")
pickles = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="pickles")


# Set objective function
m.setObjective(5*hamburgers + 1*eggs + 7*protein_bars + 6*pickles, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(11*hamburgers + 7*eggs + 7*protein_bars + 1*pickles <= 159, "dollar_cost")
m.addConstr(8*hamburgers + 14*eggs + 1*protein_bars + 4*pickles <= 87, "umami_index")
m.addConstr(5*hamburgers + 11*eggs + 10*protein_bars + 7*pickles <= 132, "healthiness_rating")
m.addConstr(7*eggs + 1*pickles >= 14, "c1")
m.addConstr(7*eggs + 7*protein_bars >= 34, "c2")
m.addConstr(11*hamburgers + 7*eggs >= 22, "c3")
m.addConstr(1*protein_bars + 4*pickles >= 20, "c4")
m.addConstr(14*eggs + 1*protein_bars >= 14, "c5")
m.addConstr(8*hamburgers + 4*pickles >= 9, "c6")
m.addConstr(14*eggs + 1*protein_bars + 4*pickles >= 21, "c7")
m.addConstr(8*hamburgers + 1*protein_bars + 4*pickles >= 21, "c8")
m.addConstr(8*hamburgers + 14*eggs + 1*protein_bars >= 21, "c9")
m.addConstr(8*hamburgers + 14*eggs + 4*pickles >= 21, "c10")
m.addConstr(14*eggs + 1*protein_bars + 4*pickles >= 10, "c11")
m.addConstr(8*hamburgers + 1*protein_bars + 4*pickles >= 10, "c12")
m.addConstr(8*hamburgers + 14*eggs + 1*protein_bars >= 10, "c13")
m.addConstr(8*hamburgers + 14*eggs + 4*pickles >= 10, "c14")
m.addConstr(14*eggs + 1*protein_bars + 4*pickles >= 15, "c15")
m.addConstr(8*hamburgers + 1*protein_bars + 4*pickles >= 15, "c16")
m.addConstr(8*hamburgers + 14*eggs + 1*protein_bars >= 15, "c17")
m.addConstr(8*hamburgers + 14*eggs + 4*pickles >= 15, "c18")
m.addConstr(11*eggs + 7*pickles >= 28, "c19")
m.addConstr(5*hamburgers + 10*protein_bars >= 17, "c20")
m.addConstr(5*hamburgers + 7*pickles >= 28, "c21")
m.addConstr(11*hamburgers + 1*pickles <= 68, "c22")
m.addConstr(7*eggs + 1*pickles <= 46, "c23")
m.addConstr(11*hamburgers + 7*protein_bars + 1*pickles <= 61, "c24")
m.addConstr(11*hamburgers + 7*eggs + 7*protein_bars <= 39, "c25")
m.addConstr(11*hamburgers + 7*eggs + 7*protein_bars + 1*pickles <= 39, "c26")
m.addConstr(14*eggs + 1*protein_bars <= 41, "c27")
m.addConstr(8*hamburgers + 1*protein_bars <= 31, "c28")
m.addConstr(1*protein_bars + 4*pickles <= 56, "c29")
m.addConstr(8*hamburgers + 14*eggs <= 40, "c30")
m.addConstr(8*hamburgers + 14*eggs + 1*protein_bars <= 41, "c31")
m.addConstr(8*hamburgers + 14*eggs + 1*protein_bars + 4*pickles <= 41, "c32")
m.addConstr(5*hamburgers + 11*eggs <= 55, "c33")
m.addConstr(5*hamburgers + 10*protein_bars + 7*pickles <= 99, "c34")
m.addConstr(5*hamburgers + 11*eggs + 7*pickles <= 101, "c35")
m.addConstr(5*hamburgers + 11*eggs + 10*protein_bars + 7*pickles <= 101, "c36")


# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    print('Obj: %g' % m.objVal)
    for v in m.getVars():
        print('%s %g' % (v.varName, v.x))
elif m.status == gp.GRB.INFEASIBLE:
    print("The problem is infeasible.")
else:
    print("The problem could not be solved to optimality.")

```