## Step 1: Define the symbolic representation of the problem

Let's define the symbolic variables:
- $x_1$ = number of perfume bottles
- $x_2$ = number of cologne bottles

The objective function to maximize profit is: $50x_1 + 60x_2$

The constraints are:
- $x_1 \geq 60$ (at least 60 perfume bottles)
- $x_2 \geq 40$ (at least 40 cologne bottles)
- $2x_1 + 2.5x_2 \leq 700$ (total time available)

## Step 2: Convert the problem into a Gurobi-compatible format

We need to express the problem in a format that can be solved by Gurobi. This involves defining the variables, the objective function, and the constraints using Gurobi's Python API.

## 3: Write down the problem in JSON format as requested

```json
{
    'sym_variables': [('x1', 'perfume bottles'), ('x2', 'cologne bottles')],
    'objective_function': '50*x1 + 60*x2',
    'constraints': ['x1 >= 60', 'x2 >= 40', '2*x1 + 2.5*x2 <= 700']
}
```

## 4: Implement the problem in Gurobi Python code

```python
import gurobi

def solve_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(lb=0, vtype=gurobi.GRB.INTEGER, name="perfume_bottles")
    x2 = model.addVar(lb=0, vtype=gurobi.GRB.INTEGER, name="cologne_bottles")

    # Set the objective function
    model.setObjective(50 * x1 + 60 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(x1 >= 60, name="perfume_min")
    model.addConstr(x2 >= 40, name="cologne_min")
    model.addConstr(2 * x1 + 2.5 * x2 <= 700, name="time_limit")

    # Update the model
    model.update()

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of perfume bottles: {x1.varValue}")
        print(f"Number of cologne bottles: {x2.varValue}")
        print(f"Max profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_problem()
```