To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints.

Let's define:
- $x_1$ as the number of chocolate croissants made.
- $x_2$ as the number of strawberry croissants made.

The objective is to maximize the total monthly profit. Given that the store makes a profit of $4 per chocolate croissant and $6 per strawberry croissant, the objective function can be represented as:
\[ \text{Maximize: } 4x_1 + 6x_2 \]

There are two main constraints:
1. The store expects to sell at most 1200 croissants in a month:
\[ x_1 + x_2 \leq 1200 \]
2. The store wants to spend at most $6000, considering it pays $3 for each chocolate croissant and $5 for each strawberry croissant:
\[ 3x_1 + 5x_2 \leq 6000 \]

Additionally, since the number of croissants cannot be negative, we have non-negativity constraints:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

Now, let's represent this problem symbolically and in code as requested:

```json
{
    'sym_variables': [('x1', 'chocolate croissants'), ('x2', 'strawberry croissants')],
    'objective_function': '4*x1 + 6*x2',
    'constraints': ['x1 + x2 <= 1200', '3*x1 + 5*x2 <= 6000', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this problem using Gurobi in Python, we'll use the following code:

```python
from gurobipy import *

# Create a new model
model = Model("Croissant_Optimization")

# Add variables to the model
x1 = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name="chocolate_croissants")
x2 = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name="strawberry_croissants")

# Set the objective function
model.setObjective(4*x1 + 6*x2, GRB.MAXIMIZE)

# Add constraints
model.addConstr(x1 + x2 <= 1200, "total_croissants")
model.addConstr(3*x1 + 5*x2 <= 6000, "budget")

# Optimize the model
model.optimize()

# Print the results
if model.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Chocolate Croissants: {x1.x}")
    print(f"Strawberry Croissants: {x2.x}")
    print(f"Total Profit: {model.ObjVal}")
else:
    print("No optimal solution found")
```