To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the problem statement.

Let's denote:
- $x_1$ as the number of taro bubble teas made,
- $x_2$ as the number of mango bubble teas made.

The objective is to maximize profit. Given that the profit per taro bubble tea is $4 and the profit per mango bubble tea is $6, the objective function can be represented as:
\[ \text{Maximize:} \quad 4x_1 + 6x_2 \]

Now, let's define the constraints based on the availability of ingredients:
- One taro bubble tea requires 3 units of taro, and there are 60 units of taro available. So, $3x_1 \leq 60$.
- One mango bubble tea requires 3 units of mango, and there are 60 units of mango available. So, $3x_2 \leq 60$.
- One taro bubble tea requires 4 units of milk, and one mango bubble tea requires 5 units of milk, with a total of 140 units of milk available. So, $4x_1 + 5x_2 \leq 140$.
- Additionally, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of bubble teas made cannot be negative.

Therefore, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'taro bubble teas'), ('x2', 'mango bubble teas')],
    'objective_function': '4*x1 + 6*x2',
    'constraints': [
        '3*x1 <= 60',
        '3*x2 <= 60',
        '4*x1 + 5*x2 <= 140',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

To solve this problem using Gurobi in Python, we can write the following code:
```python
from gurobipy import *

# Create a new model
m = Model("Bubble_Tea_Optimization")

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="taro_bubble_teas")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="mango_bubble_teas")

# Set the objective function
m.setObjective(4*x1 + 6*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*x1 <= 60, "taro_availability")
m.addConstr(3*x2 <= 60, "mango_availability")
m.addConstr(4*x1 + 5*x2 <= 140, "milk_availability")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of taro bubble teas: {x1.x}")
    print(f"Number of mango bubble teas: {x2.x}")
    print(f"Maximum profit: {m.objVal}")
else:
    print("No optimal solution found")
```