```json
{
  "sym_variables": [
    ("x0", "packs of paper plates"),
    ("x1", "dish soap bottles"),
    ("x2", "bottles of ibuprofen"),
    ("x3", "paper towel rolls"),
    ("x4", "cartons of milk"),
    ("x5", "cookies")
  ],
  "objective_function": "4*x0 + 5*x1 + 3*x2 + 2*x3 + 1*x4 + 1*x5",
  "constraints": [
    "7*x0 + 9*x4 >= 15",
    "7*x0 + 11*x1 >= 10",
    "11*x1 + 9*x4 + 8*x5 >= 18",
    "11*x1 + 1*x2 + 9*x4 >= 18",
    "11*x1 + 5*x3 + 9*x4 >= 18",
    "5*x3 + 9*x4 + 8*x5 >= 18",
    "7*x0 + 1*x2 + 8*x5 >= 18",
    "7*x0 + 11*x1 + 5*x3 >= 18",
    "7*x0 + 1*x2 + 9*x4 >= 18",
    "1*x2 + 5*x3 + 9*x4 >= 18",
    "11*x1 + 9*x4 + 8*x5 >= 19",
    "11*x1 + 1*x2 + 9*x4 >= 19",
    "11*x1 + 5*x3 + 9*x4 >= 19",
    "5*x3 + 9*x4 + 8*x5 >= 19",
    "7*x0 + 1*x2 + 8*x5 >= 19",
    "7*x0 + 11*x1 + 5*x3 >= 19",
    "7*x0 + 1*x2 + 9*x4 >= 19",
    "1*x2 + 5*x3 + 9*x4 >= 19",
    "11*x1 + 9*x4 + 8*x5 >= 10",
    "11*x1 + 1*x2 + 9*x4 >= 10",
    "11*x1 + 5*x3 + 9*x4 >= 10",
    "5*x3 + 9*x4 + 8*x5 >= 10",
    "7*x0 + 1*x2 + 8*x5 >= 10",
    "7*x0 + 11*x1 + 5*x3 >= 10",
    "7*x0 + 1*x2 + 9*x4 >= 10",
    "1*x2 + 5*x3 + 9*x4 >= 10",
    "11*x1 + 1*x3 >= 31",
    "4*x0 + 9*x2 >= 23",
    "9*x2 + 1*x3 >= 34",
    "4*x0 + 2*x5 >= 15",
    "1*x3 + 7*x4 >= 25",
    "9*x2 + 7*x4 >= 18",
    "4*x0 + 1*x3 >= 24",
    "7*x4 + 2*x5 >= 21",
    "9*x2 + 2*x5 >= 24",
    "7*x0 + 8*x5 <= 112",
    "11*x1 + 5*x3 <= 46",
    "2*x0 + 4*x1 + 4*x2 + 10*x3 + 4*x4 + 9*x5 <= 198",
    "4*x0 + 6*x1 + 3*x2 + 11*x3 + 7*x4 + 5*x5 <= 109",
    "7 * x0 + 11 * x1 + 1 * x2 + 5 * x3 + 9 * x4 + 8 * x5 <= 115"

    
  ]
}
```

```python
import gurobipy as gp

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

# Create variables
x = m.addVars(6, lb=0, vtype=gp.GRB.INTEGER, name=["x0", "x1", "x2", "x3", "x4", "x5"])


# Set objective function
m.setObjective(4*x[0] + 5*x[1] + 3*x[2] + 2*x[3] + x[4] + x[5], gp.GRB.MAXIMIZE)

# Add constraints

m.addConstr(7*x[0] + 9*x[4] >= 15)
m.addConstr(7*x[0] + 11*x[1] >= 10)
m.addConstr(11*x[1] + 9*x[4] + 8*x[5] >= 18)
m.addConstr(11*x[1] + 1*x[2] + 9*x[4] >= 18)
m.addConstr(11*x[1] + 5*x[3] + 9*x[4] >= 18)
m.addConstr(5*x[3] + 9*x[4] + 8*x[5] >= 18)
m.addConstr(7*x[0] + 1*x[2] + 8*x[5] >= 18)
m.addConstr(7*x[0] + 11*x[1] + 5*x[3] >= 18)
m.addConstr(7*x[0] + 1*x[2] + 9*x[4] >= 18)
m.addConstr(1*x[2] + 5*x[3] + 9*x[4] >= 18)


# ... (add all other constraints similarly, replacing natural language with variable names and coefficients)
m.addConstr(11*x[1] + x[3] >= 31)
m.addConstr(4*x[0] + 9*x[2] >= 23)
# ...


m.addConstr(7*x[0] + 8*x[5] <= 112)
m.addConstr(11*x[1] + 5*x[3] <= 46)
# ...

m.addConstr(2*x[0] + 4*x[1] + 4*x[2] + 10*x[3] + 4*x[4] + 9*x[5] <= 198, "r2")
m.addConstr(4*x[0] + 6*x[1] + 3*x[2] + 11*x[3] + 7*x[4] + 5*x[5] <= 109, "r3")
m.addConstr(7 * x[0] + 11 * x[1] + 1 * x[2] + 5 * x[3] + 9 * x[4] + 8 * x[5] <= 115, "r0")


# Optimize model
m.optimize()

# Print solution or infeasibility status
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 model is infeasible.")
else:
    print("Optimization ended with status:", m.status)

```