## Symbolic Representation

To solve the given problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables and the objective function, as well as the constraints.

### Variables
- $x_1$ = Number of tennis rackets
- $x_2$ = Number of badminton rackets

### Objective Function
The objective is to maximize profit. Given that the profit per tennis racket is $20 and per badminton racket is $17, the objective function can be written as:
\[ \text{Maximize:} \quad 20x_1 + 17x_2 \]

### Constraints
1. Molding time constraint: Each tennis racket takes 12 minutes to mold and each badminton racket takes 10 minutes to mold. There are 3000 minutes available for molding.
\[ 12x_1 + 10x_2 \leq 3000 \]
2. Stringing time constraint: Each tennis racket takes 15 minutes to string and each badminton racket takes 12 minutes to string. There are 3500 minutes available for stringing.
\[ 15x_1 + 12x_2 \leq 3500 \]
3. Non-negativity constraints:
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'tennis rackets'), ('x2', 'badminton rackets')],
    'objective_function': '20*x1 + 17*x2',
    'constraints': [
        '12*x1 + 10*x2 <= 3000',
        '15*x1 + 12*x2 <= 3500',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="tennis_rackets", lb=0, vtype=gp.GRB.INTEGER)
x2 = model.addVar(name="badminton_rackets", lb=0, vtype=gp.GRB.INTEGER)

# Objective function: maximize profit
model.setObjective(20*x1 + 17*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(12*x1 + 10*x2 <= 3000, name="molding_time")
model.addConstr(15*x1 + 12*x2 <= 3500, name="stringing_time")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
    print(f"Max Profit: {model.objVal}")
else:
    print("No optimal solution found")
```