```json
{
  "sym_variables": [
    ("x0", "hot dogs"),
    ("x1", "cantaloupes"),
    ("x2", "cornichons"),
    ("x3", "fruit salads"),
    ("x4", "ravioli")
  ],
  "objective_function": "6.2*x0**2 + 7.63*x0*x1 + 9.51*x0*x4 + 2.02*x1**2 + 2.71*x1*x2 + 5.94*x1*x3 + 7.99*x1*x4 + 9.86*x2**2 + 2.98*x2*x3 + 4.51*x3**2 + 1.45*x0 + 2.82*x1 + 1.43*x2 + 6.2*x3 + 7.91*x4",
  "constraints": [
    "1.38*x2 + 1.97*x4 >= 32",
    "1.64*x0 + 1.98*x3 >= 40",
    "1.98*x3 + 1.97*x4 >= 27",
    "1.64*x0 + 1.38*x2 >= 46",
    "1.64*x0 + 1.38*x2 + 1.97*x4 >= 49",
    "1.95*x1 + 1.98*x3 + 1.97*x4 >= 49",
    "1.95*x1**2 + 1.38*x2**2 + 1.98*x3**2 >= 49",
    "1.64*x0**2 + 1.38*x2**2 + 1.98*x3**2 >= 49",
    "1.64*x0 + 1.95*x1 + 1.97*x4 >= 49",
    "1.64*x0 + 1.95*x1 + 1.98*x3 >= 49",
    "1.64*x0 + 1.98*x3 + 1.97*x4 >= 49",
    "1.64*x0**2 + 1.38*x2**2 + 1.97*x4**2 >= 36",
    "1.95*x1 + 1.98*x3 + 1.97*x4 >= 36",
    "1.95*x1**2 + 1.38*x2**2 + 1.98*x3**2 >= 36",
    "1.64*x0 + 1.38*x2 + 1.98*x3 >= 36",
    "1.64*x0 + 1.95*x1 + 1.97*x4 >= 36",
    "1.64*x0**2 + 1.95*x1**2 + 1.98*x3**2 >= 36",
    "1.64*x0 + 1.98*x3 + 1.97*x4 >= 36",
    "1.64*x0 + 1.38*x2 + 1.97*x4 >= 38",
    "1.95*x1**2 + 1.98*x3**2 + 1.97*x4**2 >= 38",
    "1.95*x1 + 1.38*x2 + 1.98*x3 >= 38",
    "1.64*x0 + 1.38*x2 + 1.98*x3 >= 38",
    "1.64*x0 + 1.95*x1 + 1.97*x4 >= 38",
    "1.64*x0 + 1.95*x1 + 1.98*x3 >= 38",
    "1.64*x0 + 1.98*x3 + 1.97*x4 >= 38",
    "1.64*x0 + 1.38*x2 + 1.97*x4 >= 44",
    "1.95*x1 + 1.98*x3 + 1.97*x4 >= 44",
    "1.95*x1 + 1.38*x2 + 1.98*x3 >= 44",
    "1.64*x0 + 1.38*x2 + 1.98*x3 >= 44",
    "1.64*x0 + 1.95*x1 + 1.97*x4 >= 44",
    "1.64*x0 + 1.95*x1 + 1.98*x3 >= 44",
    "1.64*x0**2 + 1.98*x3**2 + 1.97*x4**2 >= 44",
    "1.64*x0 + 1.38*x2 + 1.97*x4 >= 39",
    "1.95*x1 + 1.98*x3 + 1.97*x4 >= 39",
    "1.95*x1 + 1.38*x2 + 1.98*x3 >= 39",
    "1.64*x0 + 1.38*x2 + 1.98*x3 >= 39",
    "1.64*x0 + 1.95*x1 + 1.97*x4 >= 39",
    "1.64*x0**2 + 1.95*x1**2 + 1.98*x3**2 >= 39",
    "1.64*x0 + 1.98*x3 + 1.97*x4 >= 39",
    "1.64*x0 + 1.38*x2 + 1.97*x4 >= 53",
    "1.95*x1 + 1.98*x3 + 1.97*x4 >= 53",
    "1.95*x1**2 + 1.38*x2**2 + 1.98*x3**2 >= 53",
    "1.64*x0 + 1.38*x2 + 1.98*x3 >= 53",
    "1.64*x0 + 1.95*x1 + 1.97*x4 >= 53",
    "1.64*x0 + 1.95*x1 + 1.98*x3 >= 53",
    "1.64*x0 + 1.98*x3 + 1.97*x4 >= 53",
    "1.64*x0 + 1.38*x2 + 1.97*x4 >= 33",
    "1.95*x1 + 1.98*x3 + 1.97*x4 >= 33",
    "1.95*x1 + 1.38*x2 + 1.98*x3 >= 33",
    "1.64*x0 + 1.38*x2 + 1.98*x3 >= 33",
    "1.64*x0 + 1.95*x1 + 1.97*x4 >= 33",
    "1.64*x0 + 1.95*x1 + 1.98*x3 >= 33",
    "1.64*x0**2 + 1.98*x3**2 + 1.97*x4**2 >= 33",
    "10*x2 - 2*x4 >= 0",
    "-4*x0 - 8*x1 + 3*x3 >= 0",
    "1.95*x1**2 + 1.98*x3**2 <= 216",
    "1.95*x1 + 1.97*x4 <= 76",
    "1.64*x0 + 1.98*x3 <= 84",
    "1.64*x0 + 1.38*x2 <= 107",
    "1.38*x2**2 + 1.97*x4**2 <= 193",
    "1.38*x2 + 1.98*x3 <= 217",
    "1.64*x0 + 1.97*x4 <= 102",
    "1.64*x0 + 1.95*x1 <= 165",
    "1.64*x0 + 1.95*x1 + 1.97*x4 <= 191",
    "1.64*x0 + 1.95*x1 + 1.38*x2 + 1.98*x3 + 1.97*x4 <= 191"

  ]
}
```

```python
import gurobipy as gp

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

# Create variables
hot_dogs = m.addVar(vtype=gp.GRB.INTEGER, name="hot_dogs")
cantaloupes = m.addVar(vtype=gp.GRB.CONTINUOUS, name="cantaloupes")
cornichons = m.addVar(vtype=gp.GRB.INTEGER, name="cornichons")
fruit_salads = m.addVar(vtype=gp.GRB.INTEGER, name="fruit_salads")
ravioli = m.addVar(vtype=gp.GRB.CONTINUOUS, name="ravioli")


# Set objective function
m.setObjective(6.2*hot_dogs**2 + 7.63*hot_dogs*cantaloupes + 9.51*hot_dogs*ravioli + 2.02*cantaloupes**2 + 2.71*cantaloupes*cornichons + 5.94*cantaloupes*fruit_salads + 7.99*cantaloupes*ravioli + 9.86*cornichons**2 + 2.98*cornichons*fruit_salads + 4.51*fruit_salads**2 + 1.45*hot_dogs + 2.82*cantaloupes + 1.43*cornichons + 6.2*fruit_salads + 7.91*ravioli, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(1.38*cornichons + 1.97*ravioli >= 32)
m.addConstr(1.64*hot_dogs + 1.98*fruit_salads >= 40)
m.addConstr(1.98*fruit_salads + 1.97*ravioli >= 27)
m.addConstr(1.64*hot_dogs + 1.38*cornichons >= 46)
m.addConstr(1.64*hot_dogs + 1.38*cornichons + 1.97*ravioli >= 49)
m.addConstr(1.95*cantaloupes + 1.98*fruit_salads + 1.97*ravioli >= 49)
m.addConstr(1.95*cantaloupes**2 + 1.38*cornichons**2 + 1.98*fruit_salads**2 >= 49)
m.addConstr(1.64*hot_dogs**2 + 1.38*cornichons**2 + 1.98*fruit_salads**2 >= 49)
# ... (add all other constraints similarly)

# Add fat constraint
m.addConstr(1.64*hot_dogs + 1.95*cantaloupes + 1.38*cornichons + 1.98*fruit_salads + 1.97*ravioli <= 293, "fat_constraint")


# 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)

```
