```json
{
  "sym_variables": [
    ("x0", "milkshakes"),
    ("x1", "oreos"),
    ("x2", "bowls of pasta"),
    ("x3", "apple pies")
  ],
  "objective_function": "9*x0 + 4*x1 + 9*x2 + 5*x3",
  "constraints": [
    "20.74*x2 + 14.49*x3 >= 87",
    "13.58*x1 + 14.49*x3 >= 68",
    "23.23*x0 + 20.74*x2 >= 104",
    "23.23*x0 + 13.58*x1 + 14.49*x3 >= 69",
    "10.41*x2 + 23.66*x3 >= 16",
    "13.58*x1 + 20.74*x2 <= 277",
    "23.23*x0 + 13.58*x1 <= 387",
    "23.23*x0 + 20.74*x2 <= 295",
    "20.74*x2 + 14.49*x3 <= 137",
    "23.23*x0 + 13.58*x1 + 14.49*x3 <= 331",
    "23.23*x0 + 13.58*x1 + 20.74*x2 <= 256",
    "23.23*x0 + 13.58*x1 + 20.74*x2 + 14.49*x3 <= 256",
    "20.53*x0 + 10.41*x2 <= 68",
    "11.23*x1 + 23.66*x3 <= 107",
    "10.41*x2 + 23.66*x3 <= 50",
    "20.53*x0 + 23.66*x3 <= 133",
    "11.23*x1 + 10.41*x2 + 23.66*x3 <= 61",
    "20.53*x0 + 11.23*x1 + 10.41*x2 <= 143",
    "20.53*x0 + 11.23*x1 + 23.66*x3 <= 157",
    "20.53*x0 + 11.23*x1 + 10.41*x2 + 23.66*x3 <= 157"
  ]
}
```

```python
import gurobipy as gp

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

# Create variables
milkshakes = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="milkshakes")
oreos = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="oreos")
bowls_of_pasta = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="bowls_of_pasta")
apple_pies = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="apple_pies")

# Set objective function
m.setObjective(9 * milkshakes + 4 * oreos + 9 * bowls_of_pasta + 5 * apple_pies, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(20.74 * bowls_of_pasta + 14.49 * apple_pies >= 87)
m.addConstr(13.58 * oreos + 14.49 * apple_pies >= 68)
m.addConstr(23.23 * milkshakes + 20.74 * bowls_of_pasta >= 104)
m.addConstr(23.23 * milkshakes + 13.58 * oreos + 14.49 * apple_pies >= 69)
m.addConstr(10.41 * bowls_of_pasta + 23.66 * apple_pies >= 16)
m.addConstr(13.58 * oreos + 20.74 * bowls_of_pasta <= 277)
m.addConstr(23.23 * milkshakes + 13.58 * oreos <= 387)
m.addConstr(23.23 * milkshakes + 20.74 * bowls_of_pasta <= 295)
m.addConstr(20.74 * bowls_of_pasta + 14.49 * apple_pies <= 137)
m.addConstr(23.23 * milkshakes + 13.58 * oreos + 14.49 * apple_pies <= 331)
m.addConstr(23.23 * milkshakes + 13.58 * oreos + 20.74 * bowls_of_pasta <= 256)
m.addConstr(23.23 * milkshakes + 13.58 * oreos + 20.74 * bowls_of_pasta + 14.49 * apple_pies <= 256)
m.addConstr(20.53 * milkshakes + 10.41 * bowls_of_pasta <= 68)
m.addConstr(11.23 * oreos + 23.66 * apple_pies <= 107)
m.addConstr(10.41 * bowls_of_pasta + 23.66 * apple_pies <= 50)
m.addConstr(20.53 * milkshakes + 23.66 * apple_pies <= 133)
m.addConstr(11.23 * oreos + 10.41 * bowls_of_pasta + 23.66 * apple_pies <= 61)
m.addConstr(20.53 * milkshakes + 11.23 * oreos + 10.41 * bowls_of_pasta <= 143)
m.addConstr(20.53 * milkshakes + 11.23 * oreos + 23.66 * apple_pies <= 157)
m.addConstr(20.53 * milkshakes + 11.23 * oreos + 10.41 * bowls_of_pasta + 23.66 * apple_pies <= 157)


# 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("The problem is infeasible.")
else:
    print("The problem could not be solved to optimality.")

```
