To solve this optimization problem, we first need to convert the natural language description into a symbolic representation. Let's denote:

- $x_1$ as the number of bottles of black milk tea.
- $x_2$ as the number of bottles of green milk tea.

The objective function aims to maximize profit. Given that each bottle of black milk tea is sold for a profit of $2.5 and each bottle of green milk tea is sold for a profit of $7, the objective function can be represented algebraically as:

\[ \text{Maximize: } 2.5x_1 + 7x_2 \]

The constraints based on the problem description are:

1. The total amount of milk used does not exceed 50,000 ml. Given that a bottle of black milk tea contains 300 ml of milk and a bottle of green milk tea contains 200 ml of milk, this constraint can be represented as:
\[ 300x_1 + 200x_2 \leq 50000 \]

2. The shop needs to make at least three times the number of bottles of black milk tea than green milk tea:
\[ x_1 \geq 3x_2 \]

3. The shop needs to make at least 10 bottles of green milk tea:
\[ x_2 \geq 10 \]

4. Non-negativity constraints, since the number of bottles cannot be negative:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

And since we're dealing with whole bottles, both $x_1$ and $x_2$ should be integers.

The symbolic representation in JSON format is:

```json
{
    'sym_variables': [('x1', 'number of bottles of black milk tea'), ('x2', 'number of bottles of green milk tea')],
    'objective_function': '2.5*x1 + 7*x2',
    'constraints': [
        '300*x1 + 200*x2 <= 50000',
        'x1 >= 3*x2',
        'x2 >= 10',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

To solve this problem using Gurobi in Python, we can use the following code:

```python
from gurobipy import *

# Create a model
m = Model("Milk_Tea_Optimization")

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="black_milk_tea")
x2 = m.addVar(vtype=GRB.INTEGER, name="green_milk_tea")

# Set objective function
m.setObjective(2.5*x1 + 7*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(300*x1 + 200*x2 <= 50000, "milk_limit")
m.addConstr(x1 >= 3*x2, "black_green_ratio")
m.addConstr(x2 >= 10, "green_minimum")
m.addConstr(x1 >= 0, "non_negative_black")
m.addConstr(x2 >= 0, "non_negative_green")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of bottles of black milk tea: {x1.x}")
    print(f"Number of bottles of green milk tea: {x2.x}")
    print(f"Maximum profit: {m.objVal}")
else:
    print("No optimal solution found")
```