```json
{
  "sym_variables": [
    ("x0", "hamburgers"),
    ("x1", "bowls of pasta"),
    ("x2", "slices of pizza"),
    ("x3", "bowls of instant ramen"),
    ("x4", "granola bars")
  ],
  "objective_function": "1*x0 + 1*x1 + 3*x2 + 6*x3 + 4*x4",
  "constraints": [
    "2*x1 + 5*x2 >= 13",
    "4*x0 + 2*x1 + 5*x2 + 5*x3 + 7*x4 >= 13",
    "1*x0 + 3*x3 >= 13",
    "1*x0 + 1*x4 >= 8",
    "3*x3 + 1*x4 >= 13",
    "1*x0 + 8*x2 + 1*x4 >= 13",
    "1*x0 + 4*x1 + 8*x2 >= 13",
    "1*x0 + 4*x1 + 3*x3 >= 13",
    "4*x1 + 3*x3 + 1*x4 >= 13",
    "4*x1 + 8*x2 + 3*x3 >= 13",
    "1*x0 + 8*x2 + 1*x4 >= 12",
    "1*x0 + 4*x1 + 8*x2 >= 12",
    "1*x0 + 4*x1 + 3*x3 >= 12",
    "4*x1 + 3*x3 + 1*x4 >= 12",
    "4*x1 + 8*x2 + 3*x3 >= 12",
    "1*x0 + 8*x2 + 1*x4 >= 14",
    "1*x0 + 4*x1 + 8*x2 >= 14",
    "1*x0 + 4*x1 + 3*x3 >= 14",
    "4*x1 + 3*x3 + 1*x4 >= 14",
    "4*x1 + 8*x2 + 3*x3 >= 14",
    "1*x0 + 8*x2 + 1*x4 >= 18",
    "1*x0 + 4*x1 + 8*x2 >= 18",
    "1*x0 + 4*x1 + 3*x3 >= 18",
    "4*x1 + 3*x3 + 1*x4 >= 18",
    "4*x1 + 8*x2 + 3*x3 >= 18",
    "1*x0 + 8*x2 + 1*x4 >= 19",
    "1*x0 + 4*x1 + 8*x2 >= 19",
    "1*x0 + 4*x1 + 3*x3 >= 19",
    "4*x1 + 3*x3 + 1*x4 >= 19",
    "4*x1 + 8*x2 + 3*x3 >= 19",
    "1*x0 + 4*x1 + 8*x2 + 3*x3 + 1*x4 >= 19",
    "-6*x1 + 8*x4 >= 0",
    "3*x0 - 6*x1 >= 0",
    "4*x0 + 5*x3 <= 91",
    "5*x2 + 7*x4 <= 74",
    "4*x0 + 7*x4 <= 102",
    "4*x0 + 2*x1 <= 91",
    "2*x1 + 7*x4 <= 58",
    "4*x0 + 2*x1 + 5*x2 <= 56",
    "4*x1 + 8*x2 <= 61",
    "1*x0 + 3*x3 <= 88",
    "4*x1 + 3*x3 <= 94",
    "1*x0 + 3*x3 + 1*x4 <= 79",
    "4*x1 + 8*x2 + 1*x4 <= 45",
    "4*x1 + 3*x3 + 1*x4 <= 102",
    "4*x0 <= 103",
    "1*x0 + 4*x1 + 8*x2 + 3*x3 + 1*x4 <= 105"
  ]
}
```

```python
import gurobipy as gp

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

# Create variables
x = m.addVars(5, vtype=gp.GRB.INTEGER, name=["hamburgers", "bowls of pasta", "slices of pizza", "bowls of instant ramen", "granola bars"])


# Set objective function
m.setObjective(1*x[0] + 1*x[1] + 3*x[2] + 6*x[3] + 4*x[4], gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(2*x[1] + 5*x[2] >= 13)
m.addConstr(4*x[0] + 2*x[1] + 5*x[2] + 5*x[3] + 7*x[4] >= 13)
m.addConstr(1*x[0] + 3*x[3] >= 13)
m.addConstr(1*x[0] + 1*x[4] >= 8)
m.addConstr(3*x[3] + 1*x[4] >= 13)
m.addConstr(1*x[0] + 8*x[2] + 1*x[4] >= 13)
m.addConstr(1*x[0] + 4*x[1] + 8*x[2] >= 13)
m.addConstr(1*x[0] + 4*x[1] + 3*x[3] >= 13)
m.addConstr(4*x[1] + 3*x[3] + 1*x[4] >= 13)
m.addConstr(4*x[1] + 8*x[2] + 3*x[3] >= 13)
m.addConstr(1*x[0] + 8*x[2] + 1*x[4] >= 12)
m.addConstr(1*x[0] + 4*x[1] + 8*x[2] >= 12)
m.addConstr(1*x[0] + 4*x[1] + 3*x[3] >= 12)
m.addConstr(4*x[1] + 3*x[3] + 1*x[4] >= 12)
m.addConstr(4*x[1] + 8*x[2] + 3*x[3] >= 12)
m.addConstr(1*x[0] + 8*x[2] + 1*x[4] >= 14)
m.addConstr(1*x[0] + 4*x[1] + 8*x[2] >= 14)
m.addConstr(1*x[0] + 4*x[1] + 3*x[3] >= 14)
m.addConstr(4*x[1] + 3*x[3] + 1*x[4] >= 14)
m.addConstr(4*x[1] + 8*x[2] + 3*x[3] >= 14)
m.addConstr(1*x[0] + 8*x[2] + 1*x[4] >= 18)
m.addConstr(1*x[0] + 4*x[1] + 8*x[2] >= 18)
m.addConstr(1*x[0] + 4*x[1] + 3*x[3] >= 18)
m.addConstr(4*x[1] + 3*x[3] + 1*x[4] >= 18)
m.addConstr(4*x[1] + 8*x[2] + 3*x[3] >= 18)
m.addConstr(1*x[0] + 8*x[2] + 1*x[4] >= 19)
m.addConstr(1*x[0] + 4*x[1] + 8*x[2] >= 19)
m.addConstr(1*x[0] + 4*x[1] + 3*x[3] >= 19)
m.addConstr(4*x[1] + 3*x[3] + 1*x[4] >= 19)
m.addConstr(4*x[1] + 8*x[2] + 3*x[3] >= 19)
m.addConstr(1*x[0] + 4*x[1] + 8*x[2] + 3*x[3] + 1*x[4] >= 19)
m.addConstr(-6*x[1] + 8*x[4] >= 0)
m.addConstr(3*x[0] - 6*x[1] >= 0)
m.addConstr(4*x[0] + 5*x[3] <= 91)
m.addConstr(5*x[2] + 7*x[4] <= 74)
m.addConstr(4*x[0] + 7*x[4] <= 102)
m.addConstr(4*x[0] + 2*x[1] <= 91)
m.addConstr(2*x[1] + 7*x[4] <= 58)
m.addConstr(4*x[0] + 2*x[1] + 5*x[2] <= 56)
m.addConstr(4*x[1] + 8*x[2] <= 61)
m.addConstr(1*x[0] + 3*x[3] <= 88)
m.addConstr(4*x[1] + 3*x[3] <= 94)
m.addConstr(1*x[0] + 3*x[3] + 1*x[4] <= 79)
m.addConstr(4*x[1] + 8*x[2] + 1*x[4] <= 45)
m.addConstr(4*x[1] + 3*x[3] + 1*x[4] <= 102)
m.addConstr(4*x[0] <= 103)
m.addConstr(1*x[0] + 4*x[1] + 8*x[2] + 3*x[3] + 1*x[4] <= 105)


# 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}")

```