## Step 1: Define the symbolic representation of the problem
Let's denote the number of blankets as $x_1$ and the number of sweaters as $x_2$. The objective is to maximize profit, where the profit per blanket is $5.50 and per sweater is $5. Therefore, the objective function can be represented as $5.50x_1 + 5x_2$.

## 2: Identify the constraints
The grandmother has limited resources: 200 units of yarn and 40 hours of knitting. A blanket requires 30 units of yarn and 5 hours of knitting, while a sweater requires 20 units of yarn and 4 hours of knitting. This translates into two constraints:
1. Yarn constraint: $30x_1 + 20x_2 \leq 200$
2. Knitting hours constraint: $5x_1 + 4x_2 \leq 40$
Additionally, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of blankets and sweaters cannot be negative.

## 3: Symbolic representation in the required format
The symbolic variables are:
- $x_1$ for blankets
- $x_2$ for sweaters

The objective function is: $5.50x_1 + 5x_2$

The constraints are:
- $30x_1 + 20x_2 \leq 200$
- $5x_1 + 4x_2 \leq 40$
- $x_1 \geq 0$
- $x_2 \geq 0$

In the required JSON format:
```json
{
'sym_variables': [('x1', 'blankets'), ('x2', 'sweaters')], 
'objective_function': '5.50*x1 + 5*x2', 
'constraints': ['30*x1 + 20*x2 <= 200', '5*x1 + 4*x2 <= 40', '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_grandmother_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="blankets", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name="sweaters", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Set the objective function
    model.setObjective(5.50 * x1 + 5 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(30 * x1 + 20 * x2 <= 200, name="yarn_constraint")
    model.addConstr(5 * x1 + 4 * x2 <= 40, name="knitting_constraint")

    # Optimize the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
        print(f"Maximum profit: ${model.objVal:.2f}")
    else:
        print("The model is infeasible")

solve_grandmother_problem()
```