To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints in terms of these variables.

Let's define:
- \(x_1\) as the area in square feet dedicated to sunflowers,
- \(x_2\) as the area in square feet dedicated to roses.

The objective is to maximize profit. The profit per square foot from sunflowers is $450, and from roses is $100. Therefore, the objective function can be written as:
\[ \text{Maximize:} \quad 450x_1 + 100x_2 \]

The constraints are:
1. The total area used cannot exceed 100 square feet:
\[ x_1 + x_2 \leq 100 \]
2. The budget for seeds is $6500. Given that sunflower seeds cost $67 per square foot and rose seeds cost $52 per square foot, we have:
\[ 67x_1 + 52x_2 \leq 6500 \]
3. Non-negativity constraints, as the area cannot be negative:
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

Therefore, the symbolic representation of the problem is:
```json
{
  'sym_variables': [('x1', 'area in square feet dedicated to sunflowers'), ('x2', 'area in square feet dedicated to roses')],
  'objective_function': '450*x1 + 100*x2',
  'constraints': ['x1 + x2 <= 100', '67*x1 + 52*x2 <= 6500', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="sunflowers_area")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="roses_area")

# Set the objective function
m.setObjective(450*x1 + 100*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 100, "total_area")
m.addConstr(67*x1 + 52*x2 <= 6500, "budget")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Area for sunflowers: {x1.x} square feet")
    print(f"Area for roses: {x2.x} square feet")
    print(f"Maximum profit: ${m.objVal}")
else:
    print("No optimal solution found.")
```