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

Let's define the symbolic variables:
- $x_1$ represents the number of long answer questions.
- $x_2$ represents the number of multiple choice questions.

The objective function to maximize the score is: $10x_1 + 2x_2$.

The constraints based on the problem description are:
1. $x_1 + x_2 \leq 15$ (at most 15 questions in total)
2. $x_1 \geq 5$ (at least 5 long answer questions)
3. $x_2 \geq 7$ (at least 7 multiple choice questions)
4. $x_1 \leq 11$ (not more than 11 long answer questions)
5. $x_2 \leq 11$ (not more than 11 multiple choice questions)
6. $x_1, x_2 \geq 0$ and are integers (non-negativity and integrality constraints)

## Step 2: Convert the problem into a Gurobi-compatible format

The symbolic representation is:
```json
{
    'sym_variables': [('x1', 'long answer questions'), ('x2', 'multiple choice questions')],
    'objective_function': '10*x1 + 2*x2',
    'constraints': [
        'x1 + x2 <= 15',
        'x1 >= 5',
        'x2 >= 7',
        'x1 <= 11',
        'x2 <= 11'
    ]
}
```

## Step 3: Write the Gurobi code in Python

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=0, ub=11, vtype=gurobi.GRB.INTEGER, name="long_answer_questions")
    x2 = model.addVar(lb=0, ub=11, vtype=gurobi.GRB.INTEGER, name="multiple_choice_questions")

    # Set the objective function
    model.setObjective(10 * x1 + 2 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(x1 + x2 <= 15, name="total_questions")
    model.addConstr(x1 >= 5, name="min_long_answer")
    model.addConstr(x2 >= 7, name="min_multiple_choice")
    model.addConstr(x1 <= 11, name="max_long_answer")
    model.addConstr(x2 <= 11, name="max_multiple_choice")

    # Optimize the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
        print(f"Maximum score: {10 * x1.varValue + 2 * x2.varValue}")
    else:
        print("The model is infeasible")

solve_optimization_problem()
```