## Problem Description and Formulation

The grandmother wants to maximize her profit by knitting blankets and sweaters. The problem can be formulated as a linear programming problem. Let's define the decision variables:

- $B$: The number of blankets to knit.
- $S$: The number of sweaters to knit.

The objective function to maximize profit is:
\[ \text{Maximize:} \quad 5.50B + 5S \]

Subject to the constraints:
1. Yarn availability: $30B + 20S \leq 200$
2. Knitting time availability: $5B + 4S \leq 40$
3. Non-negativity: $B \geq 0, S \geq 0$

## Gurobi Code

```python
import gurobi

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

    # Define the decision variables
    B = model.addVar(name="Blankets", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    S = model.addVar(name="Sweaters", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Objective function: Maximize profit
    model.setObjective(5.50 * B + 5 * S, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(30 * B + 20 * S <= 200, name="Yarn_Availability")
    model.addConstr(5 * B + 4 * S <= 40, name="Knitting_Time_Availability")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution found.")
        print(f"Blankets: {B.varValue}")
        print(f"Sweaters: {S.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found.")

if __name__ == "__main__":
    solve_grandmother_problem()
```

This code defines the optimization problem as described, using Gurobi's Python interface. It sets up the model with the correct objective function and constraints, solves it, and then prints out the optimal values for the number of blankets and sweaters to knit, along with the maximum achievable profit. If no optimal solution is found, it indicates that the problem is infeasible or unbounded.