```json
{
  "sym_variables": [
    ("x1", "number of regular hot dogs"),
    ("x2", "number of premium hot dogs")
  ],
  "objective_function": "3*x1 + 5*x2",
  "constraints": [
    "x1 <= 80",
    "x2 <= 70",
    "x1 + x2 <= 120",
    "x1 >= 0",
    "x2 >= 0"
  ]
}
```

```python
import gurobipy as gp

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

# Create variables
x1 = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="x1") # Regular hot dogs
x2 = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="x2") # Premium hot dogs


# Set objective function
m.setObjective(3*x1 + 5*x2, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 <= 80, "regular_demand")
m.addConstr(x2 <= 70, "premium_demand")
m.addConstr(x1 + x2 <= 120, "total_supply")

# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    print(f"Optimal profit: ${m.objVal}")
    print(f"Number of regular hot dogs (x1): {x1.x}")
    print(f"Number of premium hot dogs (x2): {x2.x}")
elif m.status == gp.GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization ended with status {m.status}")

```
