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

Let's denote:
- $x_1$ as the number of hoodies to be made
- $x_2$ as the number of sweaters to be made

The objective is to maximize profit, where the profit per hoodie is $20 and the profit per sweater is $15. Therefore, the objective function can be represented as:
\[ \text{Maximize:} \quad 20x_1 + 15x_2 \]

## Step 2: Define the constraints based on the given resources

Each hoodie requires 3 units of fabric and each sweater requires 2 units of fabric. Given that there are 500 units of fabric available, the fabric constraint can be represented as:
\[ 3x_1 + 2x_2 \leq 500 \]

Each hoodie requires 2 units of dye and each sweater requires 1.5 units of dye. Given that there are 300 units of dye available, the dye constraint can be represented as:
\[ 2x_1 + 1.5x_2 \leq 300 \]

Additionally, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of hoodies and sweaters to be made cannot be negative.

## 3: Symbolic representation in the required format

The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'hoodies'), ('x2', 'sweaters')],
    'objective_function': '20*x1 + 15*x2',
    'constraints': [
        '3*x1 + 2*x2 <= 500',
        '2*x1 + 1.5*x2 <= 300',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 4: Convert the problem into Gurobi code

Now, let's implement this problem using Gurobi in Python:
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=0, name="x1")  # Number of hoodies
    x2 = model.addVar(lb=0, name="x2")  # Number of sweaters

    # Define the objective function
    model.setObjective(20 * x1 + 15 * x2, gurobi.GRB.MAXIMIZE)

    # Define the constraints
    model.addConstr(3 * x1 + 2 * x2 <= 500, name="fabric_constraint")
    model.addConstr(2 * x1 + 1.5 * x2 <= 300, name="dye_constraint")

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```