To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the problem statement.

Let's define:
- $x_1$ as the number of policeman costumes.
- $x_2$ as the number of fireman costumes.

The objective function aims to maximize profit. Given that the profit per policeman costume is $8 and per fireman costume is $10, the objective function can be represented algebraically as:
\[ \text{Maximize:} \quad 8x_1 + 10x_2 \]

The constraints are based on the budget and the demand:
1. The total cost of the costumes must not exceed the budget of $3000. Given that each policeman costume costs $10 and each fireman costume costs $15, we have:
\[ 10x_1 + 15x_2 \leq 3000 \]
2. The monthly demand for both costumes will not exceed 280, so we also have:
\[ x_1 + x_2 \leq 280 \]
3. Additionally, the number of costumes cannot be negative, so we include non-negativity constraints:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

Thus, in symbolic representation, our optimization problem can be summarized as:

```json
{
  'sym_variables': [('x1', 'policeman costumes'), ('x2', 'fireman costumes')],
  'objective_function': '8*x1 + 10*x2',
  'constraints': ['10*x1 + 15*x2 <= 3000', 'x1 + x2 <= 280', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's translate this into Gurobi code in Python to solve the problem:

```python
from gurobipy import *

# Create a new model
m = Model("Costume_Store_Optimization")

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.INTEGER, name="policeman_costumes")
x2 = m.addVar(lb=0, vtype=GRB.INTEGER, name="fireman_costumes")

# Set the objective function
m.setObjective(8*x1 + 10*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(10*x1 + 15*x2 <= 3000, "Budget_Constraint")
m.addConstr(x1 + x2 <= 280, "Demand_Constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
    print(f"Maximum Profit: {m.objVal}")
else:
    print("No optimal solution found")
```