To solve this optimization problem, we first need to define the decision variables and the objective function. Let's denote:

- \(x_s\) as the number of small fish to be cleaned and cut.
- \(x_l\) as the number of large fish to be cleaned and cut.

The objective is to maximize profit. Given that each small fish generates a profit of $8 and each large fish generates a profit of $11, the objective function can be written as:

\[ \text{Maximize:} \quad 8x_s + 11x_l \]

We have two main constraints based on the time available for cleaning and cutting:

1. **Cleaning Time Constraint:** Each small fish takes 5 minutes to clean, and each large fish takes 10 minutes to clean. The total available time for cleaning is 500 minutes. Therefore, the constraint can be written as:

\[ 5x_s + 10x_l \leq 500 \]

2. **Cutting Time Constraint:** Each small fish takes 10 minutes to cut, and each large fish takes 15 minutes to cut. The total available time for cutting is 700 minutes. Therefore, the constraint can be written as:

\[ 10x_s + 15x_l \leq 700 \]

Additionally, we have non-negativity constraints since the number of fish cannot be negative:

\[ x_s \geq 0 \]
\[ x_l \geq 0 \]

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

```python
from gurobipy import *

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

# Define the decision variables
x_s = m.addVar(vtype=GRB.CONTINUOUS, name="small_fish")
x_l = m.addVar(vtype=GRB.CONTINUOUS, name="large_fish")

# Set the objective function
m.setObjective(8*x_s + 11*x_l, GRB.MAXIMIZE)

# Add constraints
m.addConstr(5*x_s + 10*x_l <= 500, "cleaning_time")
m.addConstr(10*x_s + 15*x_l <= 700, "cutting_time")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of small fish: {x_s.x}")
    print(f"Number of large fish: {x_l.x}")
    print(f"Maximum profit: ${8*x_s.x + 11*x_l.x:.2f}")
else:
    print("No optimal solution found.")
```