## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the number of cream lipsticks produced.
- $x_2$ represents the number of matte lipsticks produced.

## Step 2: Formulate the objective function
The profit per cream lipstick is $70, and the profit per matte lipstick is $100. The objective function to maximize the total monthly profit is:
\[ \text{Maximize:} \quad 70x_1 + 100x_2 \]

## 3: Define the constraints
Based on the problem description, we have the following constraints:
- It takes 3.5 hours to produce the raw materials for one cream lipstick and 5 hours for one matte lipstick, with 300 hours available per month for preparing the raw materials:
\[ 3.5x_1 + 5x_2 \leq 300 \]
- It takes 5 hours to mix one cream lipstick and 3 hours to mix one matte lipstick, with 400 hours available for mixing:
\[ 5x_1 + 3x_2 \leq 400 \]
- It takes 2 hours to pack one cream lipstick and 1.5 hours to pack one matte lipstick, with 200 hours available for packing:
\[ 2x_1 + 1.5x_2 \leq 200 \]
- Non-negativity constraints, as the number of lipsticks cannot be negative:
\[ x_1 \geq 0, x_2 \geq 0 \]

## 4: Symbolic representation of the problem
The symbolic representation is:
```json
{
'sym_variables': [('x1', 'cream lipsticks'), ('x2', 'matte lipsticks')],
'objective_function': '70*x1 + 100*x2',
'constraints': [
    '3.5*x1 + 5*x2 <= 300',
    '5*x1 + 3*x2 <= 400',
    '2*x1 + 1.5*x2 <= 200',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 5: Gurobi code
Now, let's implement this problem using Gurobi in Python:
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="cream_lipsticks", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name="matte_lipsticks", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Define the objective function
    model.setObjective(70 * x1 + 100 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(3.5 * x1 + 5 * x2 <= 300, name="raw_materials")
    model.addConstr(5 * x1 + 3 * x2 <= 400, name="mixing")
    model.addConstr(2 * x1 + 1.5 * x2 <= 200, name="packing")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Cream lipsticks: {x1.varValue}")
        print(f"Matte lipsticks: {x2.varValue}")
        print(f"Total profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_lipstick_production()
```