```json
{
  "sym_variables": [
    ("x0", "potatoes"),
    ("x1", "milkshakes"),
    ("x2", "protein bars"),
    ("x3", "hot dogs")
  ],
  "objective_function": "5.19*x0**2 + 6.13*x0*x1 + 5.47*x0*x2 + 9.83*x0*x3 + 7.3*x1**2 + 4.72*x1*x2 + 3.82*x2**2 + 8.95*x3**2 + 6.59*x0 + 6.2*x3",
  "constraints": [
    "3*x0**2 + 1*x2**2 >= 30",
    "8*x1 + 4*x3 >= 28",
    "3*x0 + 8*x1 + 1*x2 + 4*x3 >= 28",
    "3*x0 + 1*x2 <= 61",
    "3*x0 + 8*x1 <= 62",
    "3*x0 + 4*x3 <= 127",
    "3*x0 + 8*x1 + x2 + 4*x3 <= 158" 
  ]
}
```

```python
import gurobipy as gp
from gurobipy import GRB

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

# Create variables
potatoes = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="potatoes")
milkshakes = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="milkshakes")
protein_bars = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="protein_bars")
hot_dogs = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hot_dogs")


# Set objective function
m.setObjective(5.19*potatoes**2 + 6.13*potatoes*milkshakes + 5.47*potatoes*protein_bars + 9.83*potatoes*hot_dogs + 7.3*milkshakes**2 + 4.72*milkshakes*protein_bars + 3.82*protein_bars**2 + 8.95*hot_dogs**2 + 6.59*potatoes + 6.2*hot_dogs, GRB.MINIMIZE)

# Add constraints
m.addConstr(3*potatoes**2 + 1*protein_bars**2 >= 30, "c1")
m.addConstr(8*milkshakes + 4*hot_dogs >= 28, "c2")
m.addConstr(3*potatoes + 8*milkshakes + 1*protein_bars + 4*hot_dogs >= 28, "c3")
m.addConstr(3*potatoes + 1*protein_bars <= 61, "c4")
m.addConstr(3*potatoes + 8*milkshakes <= 62, "c5")
m.addConstr(3*potatoes + 4*hot_dogs <= 127, "c6")
m.addConstr(3*potatoes + 8*milkshakes + 1*protein_bars + 4*hot_dogs <= 158, "c7")


# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print('Obj: %g' % m.objVal)
    print('potatoes:', potatoes.x)
    print('milkshakes:', milkshakes.x)
    print('protein_bars:', protein_bars.x)
    print('hot_dogs:', hot_dogs.x)
elif m.status == GRB.INFEASIBLE:
    print('The model is infeasible.')
else:
    print('Optimization ended with status %d' % m.status)

```
