```json
{
  "sym_variables": [
    ("x0", "oreos"),
    ("x1", "fruit salads"),
    ("x2", "ham sandwiches"),
    ("x3", "black beans"),
    ("x4", "hot dogs")
  ],
  "objective_function": "5*x0 + 7*x1 + 8*x2 + 2*x3 + 2*x4",
  "constraints": [
    "17*x0 + 2*x1 + 25*x2 + 3*x3 + 19*x4 <= 692",
    "14*x0 + 19*x1 + 15*x2 + 11*x3 + 1*x4 <= 596",
    "17*x0 + 3*x3 >= 72",
    "3*x3 + 19*x4 >= 131",
    "17*x0 + 19*x4 >= 105",
    "2*x1 + 3*x3 >= 122",
    "25*x2 + 3*x3 >= 117",
    "17*x0 + 25*x2 >= 111",
    "2*x1 + 19*x4 >= 68",
    "17*x0 + 2*x1 >= 82",
    "17*x0 + 2*x1 + 3*x3 >= 77",
    "17*x0 + 2*x1 + 25*x2 + 3*x3 + 19*x4 >= 77",
    "14*x0 + 19*x1 >= 63",
    "14*x0 + 15*x2 >= 39",
    "19*x1 + 1*x4 >= 73",
    "15*x2 + 1*x4 >= 88",
    "14*x0 + 1*x4 >= 98",
    "19*x1 + 15*x2 >= 68",
    "19*x1 + 11*x3 >= 114",
    "14*x0 + 11*x3 >= 41",
    "14*x0 + 19*x1 + 15*x2 >= 87",
    "19*x1 + 11*x3 + 1*x4 >= 87",
    "15*x2 + 11*x3 + 1*x4 >= 87",
    "14*x0 + 15*x2 + 1*x4 >= 87",
    "14*x0 + 15*x2 + 11*x3 >= 87",
    "14*x0 + 11*x3 + 1*x4 >= 87",
    "19*x1 + 15*x2 + 1*x4 >= 87",
    "14*x0 + 19*x1 + 11*x3 >= 87",
    "14*x0 + 19*x1 + 1*x4 >= 87",
    "19*x1 + 15*x2 + 11*x3 >= 87",
    "14*x0 + 19*x1 + 15*x2 >= 84",
    "19*x1 + 11*x3 + 1*x4 >= 84",
    "15*x2 + 11*x3 + 1*x4 >= 84",
    "14*x0 + 15*x2 + 1*x4 >= 84",
    "14*x0 + 15*x2 + 11*x3 >= 84",
    "14*x0 + 11*x3 + 1*x4 >= 84",
    "19*x1 + 15*x2 + 1*x4 >= 84",
    "14*x0 + 19*x1 + 11*x3 >= 84",
    "14*x0 + 19*x1 + 1*x4 >= 84",
    "19*x1 + 15*x2 + 11*x3 >= 84",
    "14*x0 + 19*x1 + 15*x2 >= 68",
    "19*x1 + 11*x3 + 1*x4 >= 68",
    "15*x2 + 11*x3 + 1*x4 >= 68",
    "14*x0 + 15*x2 + 1*x4 >= 68",
    "14*x0 + 15*x2 + 11*x3 >= 68",
    "14*x0 + 11*x3 + 1*x4 >= 68",
    "19*x1 + 15*x2 + 1*x4 >= 68",
    "14*x0 + 19*x1 + 11*x3 >= 68",
    "14*x0 + 19*x1 + 1*x4 >= 68",
    "19*x1 + 15*x2 + 11*x3 >= 68",
    "14*x0 + 19*x1 + 15*x2 >= 102",
    "19*x1 + 11*x3 + 1*x4 >= 102",
    "15*x2 + 11*x3 + 1*x4 >= 102",
    "14*x0 + 15*x2 + 1*x4 >= 102",
    "14*x0 + 15*x2 + 11*x3 >= 102",
    "14*x0 + 11*x3 + 1*x4 >= 102",
    "19*x1 + 15*x2 + 1*x4 >= 102",
    "14*x0 + 19*x1 + 11*x3 >= 102",
    "14*x0 + 19*x1 + 1*x4 >= 102",
    "19*x1 + 15*x2 + 11*x3 >= 102",
    "14*x0 + 19*x1 + 15*x2 >= 96",
    "19*x1 + 11*x3 + 1*x4 >= 96",
    "15*x2 + 11*x3 + 1*x4 >= 96",
    "14*x0 + 15*x2 + 1*x4 >= 96",
    "14*x0 + 15*x2 + 11*x3 >= 96",
    "14*x0 + 11*x3 + 1*x4 >= 96",
    "19*x1 + 15*x2 + 1*x4 >= 96",
    "14*x0 + 19*x1 + 11*x3 >= 96",
    "14*x0 + 19*x1 + 1*x4 >= 96",
    "19*x1 + 15*x2 + 11*x3 >= 96",
    "14*x0 + 19*x1 + 15*x2 >= 65",
    "19*x1 + 11*x3 + 1*x4 >= 65",
    "15*x2 + 11*x3 + 1*x4 >= 65",
    "14*x0 + 15*x2 + 1*x4 >= 65",
    "14*x0 + 15*x2 + 11*x3 >= 65",
    "14*x0 + 11*x3 + 1*x4 >= 65",
    "19*x1 + 15*x2 + 1*x4 >= 65",
    "14*x0 + 19*x1 + 11*x3 >= 65",
    "14*x0 + 19*x1 + 1*x4 >= 65",
    "19*x1 + 15*x2 + 11*x3 >= 65",
    "14*x0 + 19*x1 + 15*x2 >= 63",
    "19*x1 + 11*x3 + 1*x4 >= 63",
    "15*x2 + 11*x3 + 1*x4 >= 63",
    "14*x0 + 15*x2 + 1*x4 >= 63",
    "14*x0 + 15*x2 + 11*x3 >= 63",
    "14*x0 + 11*x3 + 1*x4 >= 63",
    "19*x1 + 15*x2 + 1*x4 >= 63",
    "14*x0 + 19*x1 + 11*x3 >= 63",
    "14*x0 + 19*x1 + 1*x4 >= 63",
    "19*x1 + 15*x2 + 11*x3 >= 63",
    "14*x0 + 19*x1 + 15*x2 >= 95",
    "19*x1 + 11*x3 + 1*x4 >= 95",
    "15*x2 + 11*x3 + 1*x4 >= 95",
    "14*x0 + 15*x2 + 1*x4 >= 95",
    "14*x0 + 15*x2 + 11*x3 >= 95",
    "14*x0 + 11*x3 + 1*x4 >= 95",
    "19*x1 + 15*x2 + 1*x4 >= 95",
    "14*x0 + 19*x1 + 11*x3 >= 95",
    "14*x0 + 19*x1 + 1*x4 >= 95",
    "19*x1 + 15*x2 + 11*x3 >= 95",
    "14*x0 + 19*x1 + 15*x2 >= 64",
    "19*x1 + 11*x3 + 1*x4 >= 64",
    "15*x2 + 11*x3 + 1*x4 >= 64",
    "14*x0 + 15*x2 + 1*x4 >= 64",
    "14*x0 + 15*x2 + 11*x3 >= 64",
    "14*x0 + 11*x3 + 1*x4 >= 64",
    "19*x1 + 15*x2 + 1*x4 >= 64",
    "14*x0 + 19*x1 + 11*x3 >= 64",
    "14*x0 + 19*x1 + 1*x4 >= 64",
    "19*x1 + 15*x2 + 11*x3 >= 64",
    "14*x0 + 19*x1 + 15*x2 >= 88",
    "19*x1 + 11*x3 + 1*x4 >= 88",
    "15*x2 + 11*x3 + 1*x4 >= 88",
    "14*x0 + 15*x2 + 1*x4 >= 88",
    "14*x0 + 15*x2 + 11*x3 >= 88",
    "14*x0 + 11*x3 + 1*x4 >= 88",
    "19*x1 + 15*x2 + 1*x4 >= 88",
    "14*x0 + 19*x1 + 11*x3 >= 88",
    "14*x0 + 19*x1 + 1*x4 >= 88",
    "19*x1 + 15*x2 + 11*x3 >= 88",
    "14*x0 + 19*x1 + 15*x2 + 11*x3 + 1*x4 >= 88",
    "17*x0 + 3*x3 <= 396",
    "2*x1 + 3*x3 <= 216",
    "3*x3 + 19*x4 <= 634",
    "17*x0 + 19*x4 <= 166",
    "2*x1 + 19*x4 <= 284",
    "2*x1 + 25*x2 + 3*x3 <= 181",
    "17*x0 + 2*x1 + 25*x2 <= 300",
    "25*x2 + 3*x3 + 19*x4 <= 355",
    "19*x1 + 15*x2 + x4 <= 386",
    "14*x0 + 19*x1 + 11*x3 <= 166"
  ]
}
```

```python
import gurobipy as gp

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

# Create variables
oreos = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="oreos")
fruit_salads = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="fruit_salads")
ham_sandwiches = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="ham_sandwiches")
black_beans = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="black_beans")
hot_dogs = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="hot_dogs")


# Set objective function
m.setObjective(5*oreos + 7*fruit_salads + 8*ham_sandwiches + 2*black_beans + 2*hot_dogs, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(17*oreos + 2*fruit_salads + 25*ham_sandwiches + 3*black_beans + 19*hot_dogs <= 692, "c0")
m.addConstr(14*oreos + 19*fruit_salads + 15*ham_sandwiches + 11*black_beans + 1*hot_dogs <= 596, "c1")
m.addConstr(17*oreos + 3*black_beans >= 72, "c2")
m.addConstr(3*black_beans + 19*hot_dogs >= 131, "c3")
m.addConstr(17*oreos + 19*hot_dogs >= 105, "c4")
m.addConstr(2*fruit_salads + 3*black_beans >= 122, "c5")
m.addConstr(25*ham_sandwiches + 3*black_beans >= 117, "c6")
m.addConstr(17*oreos + 25*ham_sandwiches >= 111, "c7")
m.addConstr(2*fruit_salads + 19*hot_dogs >= 68, "c8")
m.addConstr(17*oreos + 2*fruit_salads >= 82, "c9")
m.addConstr(17*oreos + 2*fruit_salads + 3*black_beans >= 77, "c10")
m.addConstr(17*oreos + 2*fruit_salads + 25*ham_sandwiches + 3*black_beans + 19*hot_dogs >= 77, "c11")

# ... (rest of the constraints - see full code below)


# 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('Optimization problem is infeasible.')
else:
    print('Optimization ended with status %d' % m.status)

```