```json
{
  "sym_variables": [
    ("x0", "rotisserie chickens"),
    ("x1", "cornichons"),
    ("x2", "ravioli"),
    ("x3", "pickles")
  ],
  "objective_function": "8*x0 + 3*x1 + 1*x2 + 9*x3",
  "constraints": [
    "8*x0 + 3*x3 >= 35",
    "8*x0 + 17*x2 >= 35",
    "12*x1 + 17*x2 >= 28",
    "12*x1 + 3*x3 >= 18",
    "8*x0 + 12*x1 + 17*x2 + 3*x3 >= 18",
    "17*x2 + 12*x3 >= 40",
    "5*x0 + 17*x2 >= 44",
    "5*x0 + 17*x2 + 12*x3 >= 52",
    "5*x0 + 3*x1 + 12*x3 >= 52",
    "3*x1 + 17*x2 + 12*x3 >= 52",
    "5*x0 + 17*x2 + 12*x3 >= 51",
    "5*x0 + 3*x1 + 12*x3 >= 51",
    "3*x1 + 17*x2 + 12*x3 >= 51",
    "5*x0 + 17*x2 + 12*x3 >= 49",
    "5*x0 + 3*x1 + 12*x3 >= 49",
    "3*x1 + 17*x2 + 12*x3 >= 49",
    "5*x0 + 3*x1 + 17*x2 + 12*x3 >= 49",
    "10*x1 - 8*x2 >= 0",
    "1*x1 - 3*x3 >= 0",
    "-8*x0 + 9*x2 >= 0",
    "8*x0 + 12*x1 + 3*x3 <= 99",
    "8*x0 + 17*x2 + 3*x3 <= 130",
    "12*x1 + 17*x2 + 3*x3 <= 52",
    "5*x0 + 3*x1 + 12*x3 <= 176",
    "x0 >= 0",
    "x1 >= 0",
    "x2 >= 0",
    "x3 >= 0"
  ]
}
```

```python
import gurobipy as gp

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

# Create variables
x = m.addVars(4, lb=0, vtype=gp.GRB.CONTINUOUS, names=["rotisserie_chickens", "cornichons", "ravioli", "pickles"])

# Set objective function
m.setObjective(8*x[0] + 3*x[1] + 1*x[2] + 9*x[3], gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(8*x[0] + 3*x[3] >= 35)
m.addConstr(8*x[0] + 17*x[2] >= 35)
m.addConstr(12*x[1] + 17*x[2] >= 28)
m.addConstr(12*x[1] + 3*x[3] >= 18)
m.addConstr(8*x[0] + 12*x[1] + 17*x[2] + 3*x[3] >= 18)
m.addConstr(17*x[2] + 12*x[3] >= 40)
m.addConstr(5*x[0] + 17*x[2] >= 44)
m.addConstr(5*x[0] + 17*x[2] + 12*x[3] >= 52)
m.addConstr(5*x[0] + 3*x[1] + 12*x[3] >= 52)
m.addConstr(3*x[1] + 17*x[2] + 12*x[3] >= 52)
m.addConstr(5*x[0] + 17*x[2] + 12*x[3] >= 51)
m.addConstr(5*x[0] + 3*x[1] + 12*x[3] >= 51)
m.addConstr(3*x[1] + 17*x[2] + 12*x[3] >= 51)
m.addConstr(5*x[0] + 17*x[2] + 12*x[3] >= 49)
m.addConstr(5*x[0] + 3*x[1] + 12*x[3] >= 49)
m.addConstr(3*x[1] + 17*x[2] + 12*x[3] >= 49)
m.addConstr(5*x[0] + 3*x[1] + 17*x[2] + 12*x[3] >= 49)
m.addConstr(10*x[1] - 8*x[2] >= 0)
m.addConstr(1*x[1] - 3*x[3] >= 0)
m.addConstr(-8*x[0] + 9*x[2] >= 0)
m.addConstr(8*x[0] + 12*x[1] + 3*x[3] <= 99)
m.addConstr(8*x[0] + 17*x[2] + 3*x[3] <= 130)
m.addConstr(12*x[1] + 17*x[2] + 3*x[3] <= 52)
m.addConstr(5*x[0] + 3*x[1] + 12*x[3] <= 176)


# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    for v in m.getVars():
        print(f"{v.varName}: {v.x}")
    print(f"Obj: {m.objVal}")
elif m.status == gp.GRB.INFEASIBLE:
    print("The problem is infeasible.")
else:
    print(f"Optimization ended with status {m.status}")

```
