```json
{
  "sym_variables": [
    ("x0", "cartons of milk"),
    ("x1", "packs of napkins"),
    ("x2", "paper towel rolls"),
    ("x3", "cookies")
  ],
  "objective_function": "1*x0 + 7*x1 + 3*x2 + 4*x3",
  "constraints": [
    "5*x0 + 8*x1 + 7*x2 + 2*x3 <= 32",
    "2*x0 + 4*x1 + 6*x2 + 7*x3 <= 77",
    "8*x1 + 7*x2 >= 4",
    "5*x0 + 7*x2 >= 8",
    "5*x0 + 8*x1 + 7*x2 + 2*x3 >= 8",
    "2*x0 + 6*x2 >= 10",
    "2*x0 + 7*x3 >= 11",
    "4*x1 + 6*x2 >= 10",
    "6*x2 + 7*x3 >= 13",
    "2*x0 + 4*x1 + 7*x3 >= 14",
    "4*x1 + 6*x2 + 7*x3 >= 14",
    "2*x0 + 4*x1 + 7*x3 >= 13",
    "4*x1 + 6*x2 + 7*x3 >= 13",
    "2*x0 + 4*x1 + 6*x2 + 7*x3 >= 13",
    "4*x0 - 8*x2 >= 0",
    "-8*x0 + 10*x1 >= 0",
    "8*x1 + 2*x3 <= 12",
    "5*x0 + 8*x1 <= 20",
    "6*x2 + 7*x3 <= 53",
    "2*x0 + 7*x3 <= 72",
    "2*x0 + 6*x2 <= 46",
    "4*x1 + 6*x2 <= 46",
    "2*x0 + 4*x1 + 7*x3 <= 19"
  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    x = m.addVars(4, vtype=gp.GRB.INTEGER, name=["x0", "x1", "x2", "x3"])


    # Set objective function
    m.setObjective(1*x[0] + 7*x[1] + 3*x[2] + 4*x[3], gp.GRB.MINIMIZE)

    # Add constraints
    m.addConstr(5*x[0] + 8*x[1] + 7*x[2] + 2*x[3] <= 32, "c0")
    m.addConstr(2*x[0] + 4*x[1] + 6*x[2] + 7*x[3] <= 77, "c1")
    m.addConstr(8*x[1] + 7*x[2] >= 4, "c2")
    m.addConstr(5*x[0] + 7*x[2] >= 8, "c3")
    m.addConstr(5*x[0] + 8*x[1] + 7*x[2] + 2*x[3] >= 8, "c4")
    m.addConstr(2*x[0] + 6*x[2] >= 10, "c5")
    m.addConstr(2*x[0] + 7*x[3] >= 11, "c6")
    m.addConstr(4*x[1] + 6*x[2] >= 10, "c7")
    m.addConstr(6*x[2] + 7*x[3] >= 13, "c8")
    m.addConstr(2*x[0] + 4*x[1] + 7*x[3] >= 14, "c9")
    m.addConstr(4*x[1] + 6*x[2] + 7*x[3] >= 14, "c10")
    m.addConstr(2*x[0] + 4*x[1] + 7*x[3] >= 13, "c11")
    m.addConstr(4*x[1] + 6*x[2] + 7*x[3] >= 13, "c12")
    m.addConstr(2*x[0] + 4*x[1] + 6*x[2] + 7*x[3] >= 13, "c13")
    m.addConstr(4*x[0] - 8*x[2] >= 0, "c14")
    m.addConstr(-8*x[0] + 10*x[1] >= 0, "c15")
    m.addConstr(8*x[1] + 2*x[3] <= 12, "c16")
    m.addConstr(5*x[0] + 8*x[1] <= 20, "c17")
    m.addConstr(6*x[2] + 7*x[3] <= 53, "c18")
    m.addConstr(2*x[0] + 7*x[3] <= 72, "c19")
    m.addConstr(2*x[0] + 6*x[2] <= 46, "c20")
    m.addConstr(4*x[1] + 6*x[2] <= 46, "c21")
    m.addConstr(2*x[0] + 4*x[1] + 7*x[3] <= 19, "c22")


    # Optimize model
    m.optimize()

    if m.status == gp.GRB.OPTIMAL:
        for v in m.getVars():
            print('%s %g' % (v.varName, v.x))
        print('Obj: %g' % m.objVal)
    elif m.status == gp.GRB.INFEASIBLE:
        print('The problem is infeasible.')


except gp.GurobiError as e:
    print('Error code ' + str(e.errno) + ': ' + str(e))

except AttributeError:
    print('Encountered an attribute error')
```