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

Let's define the symbolic variables:
- $x_1$ = number of multiple choice questions
- $x_2$ = number of short answer questions

The objective is to maximize the score, where multiple choice questions are worth 2 points each and short answer questions are worth 5 points each. Therefore, the objective function can be represented as:
\[ \text{Maximize:} \quad 2x_1 + 5x_2 \]

## Step 2: List the constraints

The constraints based on the problem description are:
1. Nolan can answer at most 30 questions: $x_1 + x_2 \leq 30$
2. Nolan must answer at least 15 multiple choice questions: $x_1 \geq 15$
3. Nolan must answer at least 10 short answer questions: $x_2 \geq 10$
4. Nolan can answer at most 20 multiple choice questions: $x_1 \leq 20$
5. Nolan can answer at most 20 short answer questions: $x_2 \leq 20$

## 3: Symbolic representation in JSON format

```json
{
    'sym_variables': [('x1', 'multiple choice questions'), ('x2', 'short answer questions')],
    'objective_function': '2*x1 + 5*x2',
    'constraints': [
        'x1 + x2 <= 30',
        'x1 >= 15',
        'x2 >= 10',
        'x1 <= 20',
        'x2 <= 20'
    ]
}
```

## 4: Gurobi code in Python

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=0, ub=20, name="multiple_choice")
    x2 = model.addVar(lb=0, ub=20, name="short_answer")

    # Set objective function
    model.setObjective(2*x1 + 5*x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(x1 + x2 <= 30, name="total_questions")
    model.addConstr(x1 >= 15, name="min_multiple_choice")
    model.addConstr(x2 >= 10, name="min_short_answer")
    model.addConstr(x1 <= 20, name="max_multiple_choice")
    model.addConstr(x2 <= 20, name="max_short_answer")

    # Update model
    model.update()

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution:")
        print(f"Multiple choice questions: {x1.varValue}")
        print(f"Short answer questions: {x2.varValue}")
        print(f"Max score: {2*x1.varValue + 5*x2.varValue}")
    else:
        print("No optimal solution found.")

nolan_physics_contest()
```