To solve the optimization problem described, we first need to define the variables and parameters involved. Let's denote:
- $x$ as the number of mini elephants made,
- $y$ as the number of mini lions made.

The objective is to maximize profit. Given that each mini elephant brings in $50 and each mini lion brings in $45, the total profit can be represented by the function: $50x + 45y$.

There are two constraints based on the problem description:
1. **Clay Availability Constraint**: Each mini elephant requires 10 units of clay, and each mini lion requires 8 units of clay. The artist has a maximum of 300 units of clay available. This constraint can be represented as $10x + 8y \leq 300$.
2. **Time Constraints**: The artist can make at most 33 animals in total. This constraint can be represented as $x + y \leq 33$.

Additionally, we should note that the number of mini elephants and lions cannot be negative since these represent quantities of physical items, so $x \geq 0$ and $y \geq 0$.

Now, let's translate this into Gurobi code in Python. We will use the `gurobipy` library to model and solve this linear programming problem.

```python
from gurobipy import *

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

# Define variables
x = m.addVar(name="mini_elephants", lb=0, vtype=GRB.CONTINUOUS)
y = m.addVar(name="mini_lions", lb=0, vtype=GRB.CONTINUOUS)

# Set the objective function: Maximize profit
m.setObjective(50*x + 45*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(10*x + 8*y <= 300, name="clay_availability")
m.addConstr(x + y <= 33, name="time_constraint")

# Optimize the model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: x = {x.x}, y = {y.x}")
    print(f"Maximum profit: ${50*x.x + 45*y.x:.2f}")
else:
    print("No optimal solution found")

```