## Symbolic Representation

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

Let's denote:
- \(x_1\) as the number of lenses sold
- \(x_2\) as the number of tripods sold

The objective is to maximize profit. The profit per lens sold is $200, and the profit per tripod sold is $150. Therefore, the objective function can be represented as:
\[ \text{Maximize:} \quad 200x_1 + 150x_2 \]

The constraints given are:
1. The store can spend at most $10,000 on camera equipment. Each lens costs $400, and each tripod costs $300.
\[ 400x_1 + 300x_2 \leq 10000 \]
2. At least 10 lenses but at most 25 are sold each month.
\[ 10 \leq x_1 \leq 25 \]
3. The number of tripods sold is at most a third of the number of lenses sold.
\[ x_2 \leq \frac{1}{3}x_1 \]

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'lenses'), ('x2', 'tripods')],
    'objective_function': '200*x1 + 150*x2',
    'constraints': [
        '400*x1 + 300*x2 <= 10000',
        '10 <= x1 <= 25',
        'x2 <= (1/3)*x1'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(lb=10, ub=25, name="lenses")  # At least 10 lenses but at most 25
    x2 = model.addVar(name="tripods")

    # Objective function: Maximize 200*x1 + 150*x2
    model.setObjective(200*x1 + 150*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(400*x1 + 300*x2 <= 10000, name="budget_constraint")  # Budget constraint
    model.addConstr(x2 <= (1/3)*x1, name="tripod_lens_ratio_constraint")  # Tripod to lens ratio constraint

    # Update model
    model.update()

    # Optimize model
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Lenses: {x1.varValue}")
        print(f"Tripods: {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_camera_store_problem()
```