To solve the given optimization problem, 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 mini bears made,
- $x_2$ as the number of mini dogs made.

The objective is to maximize profit, with each mini bear sold giving a profit of $40 and each mini dog giving a profit of $47. Thus, the objective function can be written as:
\[ \text{Maximize:} \quad 40x_1 + 47x_2 \]

Now, let's consider the constraints:
1. Each mini bear requires 8 units of cotton, and each mini dog requires 7 units of cotton. The artist has 400 units of cotton available.
\[ 8x_1 + 7x_2 \leq 400 \]
2. The artist can make at most 40 animals in total.
\[ x_1 + x_2 \leq 40 \]
3. The number of mini bears and mini dogs cannot be negative (non-negativity constraint).
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

In symbolic notation with natural language objects, we have:
```json
{
    'sym_variables': [('x1', 'mini bears'), ('x2', 'mini dogs')],
    'objective_function': '40*x1 + 47*x2',
    'constraints': [
        '8*x1 + 7*x2 <= 400',
        'x1 + x2 <= 40',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

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

```python
from gurobipy import *

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

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

# Set the objective function
m.setObjective(40*x1 + 47*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(8*x1 + 7*x2 <= 400, "cotton_constraint")
m.addConstr(x1 + x2 <= 40, "total_animals_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Mini bears: {x1.x}")
    print(f"Mini dogs: {x2.x}")
    print(f"Maximum profit: ${40*x1.x + 47*x2.x}")
else:
    print("No optimal solution found")
```