## Symbolic Representation

To solve the given problem, we first need to convert the natural language description into a symbolic representation.

Let's define the variables:
- $x_1$ = number of small shelves
- $x_2$ = number of large shelves

The objective is to maximize the number of action figures, which can be represented as:
- $20x_1 + 30x_2$ (since a small shelf can hold 20 action figures and a large shelf can hold 30 action figures)

The constraints are:
- $3x_1 + 6x_2 \leq 100$ (space constraint: 3 sq ft for small shelf and 6 sq ft for large shelf, with 100 sq ft available)
- $50x_1 + 80x_2 \leq 1250$ (budget constraint: $50 for small shelf and $80 for large shelf, with $1250 budget)
- $x_1 \geq 0$ and $x_2 \geq 0$ (non-negativity constraints: can't buy negative number of shelves)

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'small shelves'), ('x2', 'large shelves')],
    'objective_function': '20*x1 + 30*x2',
    'constraints': [
        '3*x1 + 6*x2 <= 100',
        '50*x1 + 80*x2 <= 1250',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("shelf_optimization")

# Define variables
x1 = model.addVar(name="small_shelves", lb=0, vtype=gp.GRB.INTEGER)  # Number of small shelves
x2 = model.addVar(name="large_shelves", lb=0, vtype=gp.GRB.INTEGER)  # Number of large shelves

# Objective function: Maximize the number of action figures
model.setObjective(20*x1 + 30*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(3*x1 + 6*x2 <= 100, name="space_constraint")  # Space constraint
model.addConstr(50*x1 + 80*x2 <= 1250, name="budget_constraint")  # Budget constraint

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
    print(f"Maximum number of action figures: {20*x1.x + 30*x2.x}")
else:
    print("No optimal solution found")
```