## Symbolic Representation

To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation.

Let's define the symbolic variables as follows:

- $x_1$ = Number of cups of green tea
- $x_2$ = Number of cups of black tea

The objective is to maximize profit. The profit on each cup of green tea is $2, and on each cup of black tea is $3. Therefore, the objective function can be represented as:

Maximize: $2x_1 + 3x_2$

The constraints given are:

1. Time constraint: It takes 3 minutes to make a cup of green tea and 5 minutes to make a cup of black tea, with a total of 560 minutes available per week.
   - $3x_1 + 5x_2 \leq 560$

2. Product constraint: The owner only has enough product to make 150 total cups per week.
   - $x_1 + x_2 \leq 150$

3. Non-negativity constraint: The number of cups cannot be negative.
   - $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'cups of green tea'), ('x2', 'cups of black tea')],
    'objective_function': '2*x1 + 3*x2',
    'constraints': [
        '3*x1 + 5*x2 <= 560',
        'x1 + x2 <= 150',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define variables
x1 = m.addVar(name="green_tea", lb=0, vtype=gp.GRB.INTEGER)  # cups of green tea
x2 = m.addVar(name="black_tea", lb=0, vtype=gp.GRB.INTEGER)  # cups of black tea

# Objective function: Maximize profit
m.setObjective(2 * x1 + 3 * x2, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(3 * x1 + 5 * x2 <= 560, name="time_constraint")  # time constraint
m.addConstr(x1 + x2 <= 150, name="product_constraint")  # product constraint

# Solve the model
m.solve()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: Green Tea = {x1.varValue}, Black Tea = {x2.varValue}")
    print(f"Max Profit: {m.objVal}")
else:
    print("No optimal solution found")
```")
```