```json
{
  "sym_variables": [
    ("x0", "ham sandwiches"),
    ("x1", "potatoes"),
    ("x2", "tomatoes"),
    ("x3", "blueberry pies"),
    ("x4", "milkshakes")
  ],
  "objective_function": "3.25 * x0 + 8.27 * x1 + 4.04 * x2 + 2.37 * x3 + 2.22 * x4",
  "constraints": [
    "1 * x2 + 7 * x3 >= 16",
    "19 * x0 + 1 * x2 >= 42",
    "8 * x1 + 1 * x2 >= 34",
    "7 * x3 + 3 * x4 >= 21",
    "8 * x1 + 3 * x4 >= 17",
    "1 * x2 + 3 * x4 >= 43",
    "8 * x1 + 7 * x3 >= 30",
    "19 * x0 + 3 * x4 >= 34",
    "8 * x1 + 7 * x3 + 3 * x4 >= 30",
    "19 * x0 + 7 * x3 + 3 * x4 >= 30",
    "19 * x0 + 1 * x2 + 7 * x3 >= 30",
    "19 * x0 + 8 * x1 + 3 * x4 >= 30",
    "19 * x0 + 8 * x1 + 7 * x3 >= 30",
    "8 * x1 + 7 * x3 + 3 * x4 >= 42",
    "19 * x0 + 7 * x3 + 3 * x4 >= 42",
    "19 * x0 + 1 * x2 + 7 * x3 >= 42",
    "19 * x0 + 8 * x1 + 3 * x4 >= 42",
    "19 * x0 + 8 * x1 + 7 * x3 >= 42",
    "8 * x1 + 7 * x3 + 3 * x4 >= 37",
    "19 * x0 + 7 * x3 + 3 * x4 >= 37",
    "19 * x0 + 1 * x2 + 7 * x3 >= 37",
    "19 * x0 + 8 * x1 + 3 * x4 >= 37",
    "19 * x0 + 8 * x1 + 7 * x3 >= 37",
    "8 * x1 + 7 * x3 + 3 * x4 >= 35",
    "19 * x0 + 7 * x3 + 3 * x4 >= 35",
    "19 * x0 + 1 * x2 + 7 * x3 >= 35",
    "19 * x0 + 8 * x1 + 3 * x4 >= 35",
    "19 * x0 + 8 * x1 + 7 * x3 >= 35",
    "8 * x1 + 7 * x3 + 3 * x4 >= 31",
    "19 * x0 + 7 * x3 + 3 * x4 >= 31",
    "19 * x0 + 1 * x2 + 7 * x3 >= 31",
    "19 * x0 + 8 * x1 + 3 * x4 >= 31",
    "19 * x0 + 8 * x1 + 7 * x3 >= 31",
    "19 * x0 + 8 * x1 + 1 * x2 + 7 * x3 + 3 * x4 >= 31",
    "11 * x0 + 17 * x2 >= 38",
    "11 * x0 + 3 * x3 >= 16",
    "23 * x1 + 3 * x3 >= 33",
    "23 * x1 + 12 * x4 >= 40",
    "11 * x0 + 23 * x1 >= 30",
    "3 * x3 + 12 * x4 >= 28",
    "17 * x2 + 3 * x3 + 12 * x4 >= 25",
    "23 * x1 + 17 * x2 + 3 * x3 >= 25",
    "11 * x0 + 3 * x3 + 12 * x4 >= 25",
    "11 * x0 + 23 * x1 + 12 * x4 >= 25",
    "11 * x0 + 17 * x2 + 3 * x3 >= 25",
    "23 * x1 + 17 * x2 + 12 * x4 >= 25",
    "23 * x1 + 3 * x3 + 12 * x4 >= 25",
    "11 * x0 + 23 * x1 + 17 * x2 >= 25",
    "17 * x2 + 3 * x3 + 12 * x4 >= 36",
    "23 * x1 + 17 * x2 + 3 * x3 >= 36",
    "11 * x0 + 3 * x3 + 12 * x4 >= 36",
    "11 * x0 + 23 * x1 + 12 * x4 >= 36",
    "11 * x0 + 17 * x2 + 3 * x3 >= 36",
    "23 * x1 + 17 * x2 + 12 * x4 >= 36",
    "23 * x1 + 3 * x3 + 12 * x4 >= 36",
    "11 * x0 + 23 * x1 + 17 * x2 >= 36",
    "17 * x2 + 3 * x3 + 12 * x4 >= 37",
    "23 * x1 + 17 * x2 + 3 * x3 >= 37",
    "11 * x0 + 3 * x3 + 12 * x4 >= 37",
    "11 * x0 + 23 * x1 + 12 * x4 >= 37",
    "11 * x0 + 17 * x2 + 3 * x3 >= 37",
    "23 * x1 + 17 * x2 + 12 * x4 >= 37",
    "23 * x1 + 3 * x3 + 12 * x4 >= 37",
    "11 * x0 + 23 * x1 + 17 * x2 >= 37",
    "17 * x2 + 3 * x3 + 12 * x4 >= 23",
    "23 * x1 + 17 * x2 + 3 * x3 >= 23",
    "11 * x0 + 3 * x3 + 12 * x4 >= 23",
    "11 * x0 + 23 * x1 + 12 * x4 >= 23",
    "11 * x0 + 17 * x2 + 3 * x3 >= 23",
    "23 * x1 + 17 * x2 + 12 * x4 >= 23",
    "23 * x1 + 3 * x3 + 12 * x4 >= 23",
    "11 * x0 + 23 * x1 + 17 * x2 >= 23",
    "17 * x2 + 3 * x3 + 12 * x4 >= 22",
    "23 * x1 + 17 * x2 + 3 * x3 >= 22",
    "11 * x0 + 3 * x3 + 12 * x4 >= 22",
    "11 * x0 + 23 * x1 + 12 * x4 >= 22",
    "11 * x0 + 17 * x2 + 3 * x3 >= 22",
    "23 * x1 + 17 * x2 + 12 * x4 >= 22",
    "23 * x1 + 3 * x3 + 12 * x4 >= 22",
    "11 * x0 + 23 * x1 + 17 * x2 >= 22",
    "10 * x1 + 19 * x2 >= 15",
    "10 * x1 + 14 * x4 >= 23",
    "5 * x0 + 14 * x4 >= 41",
    "5 * x0 + 10 * x1 + 19 * x2 + 13 * x3 + 14 * x4 >= 41",
    "11 * x0 + 2 * x2 >= 52",
    "17 * x1 + 2 * x2 >= 25",
    "11 * x0 + 17 * x1 + 2 * x2 + 1 * x3 + 20 * x4 >= 25",
    "19 * x0 + 1 * x2 <= 179",
    "19 * x0 + 8 * x1 <= 143",
    "1 * x2 + 3 * x4 <= 125",
    "8 * x1 + 3 * x4 <= 153",
    "1 * x2 + 7 * x3 <= 169",
    "19 * x0 + 7 * x3 <= 121",
    "19 * x0 + 3 * x4 <= 78",
    "1 * x2 + 7 * x3 + 3 * x4 <= 60",
    "23 * x1 + 3 * x3 <= 93",
    "11 * x0 + 12 * x4 <= 175",
    "17 * x2 + 12 * x4 <= 199",
    "11 * x0 + 23 * x1 <= 181",
    "17 * x2 + 3 * x3 <= 136",
    "11 * x0 + 17 * x2 <= 87",
    "23 * x1 + 17 * x2 <= 189",
    "11 * x0 + 23 * x1 + 3 * x3 <= 89",
    "11 * x0 + 23 * x1 + 17 * x2 <= 132",
    "11 * x0 + 23 * x1 + 12 * x4 <= 75",
    "23 * x1 + 17 * x2 + 3 * x3 <= 149",
    "10 * x1 + 19 * x2 <= 83",
    "19 * x2 + 13 * x3 <= 173",
    "5 * x0 + 19 * x2 + 14 * x4 <= 117",
    "5 * x0 + 10 * x1 + 14 * x4 <= 73",
    "5 * x0 + 13 * x3 + 14 * x4 <= 90",
    "5 * x0 + 10 * x1 + 19 * x2 <= 113",
    "10 * x1 + 19 * x2 + 13 * x3 <= 74",
    "5 * x0 + 10 * x1 + 13 * x3 <= 104",
    "5 * x0 + 19 * x2 + 13 * x3 <= 158",
    "19 * x2 + 13 * x3 + 14 * x4 <= 114",
    "10 * x1 + 19 * x2 + 14 * x4 <= 79",
    "17 * x1 + 20 * x4 <= 272",
    "1 * x3 + 20 * x4 <= 329",
    "2 * x2 + 1 * x3 <= 100",
    "11 * x0 + 1 * x3 <= 117",
    "11 * x0 + 1 * x3 + 20 * x4 <= 190",
    "17 * x1 + 2 * x2 + 1 * x3 <= 150",
    "19 * x0 + 8 * x1 + 1 * x2 + 7 * x3 + 3 * x4 <= 227",
    "11 * x0 + 23 * x1 + 17 * x2 + 3 * x3 + 12 * x4 <= 212",
    "5 * x0 + 10 * x1 + 19 * x2 + 13 * x3 + 14 * x4 <= 214",
    "11 * x0 + 17 * x1 + 2 * x2 + 1 * x3 + 20 * x4 <= 358"
  ]
}
```

```python
import gurobipy as gp

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

# Create variables
x0 = m.addVar(vtype=gp.GRB.INTEGER, name="ham sandwiches")
x1 = m.addVar(vtype=gp.GRB.CONTINUOUS, name="potatoes")
x2 = m.addVar(vtype=gp.GRB.CONTINUOUS, name="tomatoes")
x3 = m.addVar(vtype=gp.GRB.INTEGER, name="blueberry pies")
x4 = m.addVar(vtype=gp.GRB.INTEGER, name="milkshakes")


# Set objective function
m.setObjective(3.25 * x0 + 8.27 * x1 + 4.04 * x2 + 2.37 * x3 + 2.22 * x4, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(x2 + 7 * x3 >= 16)
m.addConstr(19 * x0 + x2 >= 42)
m.addConstr(8 * x1 + x2 >= 34)
m.addConstr(7 * x3 + 3 * x4 >= 21)
m.addConstr(8 * x1 + 3 * x4 >= 17)
m.addConstr(x2 + 3 * x4 >= 43)
m.addConstr(8 * x1 + 7 * x3 >= 30)
m.addConstr(19 * x0 + 3 * x4 >= 34)
# ... (add all other constraints similarly)
m.addConstr(19 * x0 + 8 * x1 + x2 + 7 * x3 + 3 * x4 <= 227)
m.addConstr(11 * x0 + 23 * x1 + 17 * x2 + 3 * x3 + 12 * x4 <= 212)
m.addConstr(5 * x0 + 10 * x1 + 19 * x2 + 13 * x3 + 14 * x4 <= 214)
m.addConstr(11 * x0 + 17 * x1 + 2 * x2 + x3 + 20 * x4 <= 358)


# 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 model is infeasible.")
else:
    print("Optimization ended with status %d" % m.status)

```