To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables as follows:

- $x_1$: The number of pieces of fried fish to sell.
- $x_2$: The number of pieces of fried chicken to sell.

The objective function, which represents the total revenue, can be written as:
\[ 4x_1 + 5x_2 \]

This is because each piece of fried fish generates $4 in revenue and each piece of fried chicken generates $5 in revenue.

The constraints based on the available resources (batter and oil) are:
1. Batter constraint: $3x_1 + 4x_2 \leq 400$ (since each piece of fried fish requires 3 units of batter and each piece of fried chicken requires 4 units, and there are 400 units of batter available).
2. Oil constraint: $5x_1 + 6x_2 \leq 500$ (since each piece of fried fish requires 5 units of oil and each piece of fried chicken requires 6 units, and there are 500 units of oil available).

Additionally, the non-negativity constraints are:
- $x_1 \geq 0$
- $x_2 \geq 0$

These constraints ensure that the number of pieces of fried fish and fried chicken to sell are not negative.

The symbolic representation of the problem can be summarized as:
```json
{
    'sym_variables': [('x1', 'number of pieces of fried fish'), ('x2', 'number of pieces of fried chicken')],
    'objective_function': '4*x1 + 5*x2',
    'constraints': ['3*x1 + 4*x2 <= 400', '5*x1 + 6*x2 <= 500', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this optimization problem using Gurobi in Python:
```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="fried_fish")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="fried_chicken")

# Set the objective function
m.setObjective(4*x1 + 5*x2, GRB.MAXIMIZE)

# Add the constraints
m.addConstr(3*x1 + 4*x2 <= 400, "batter_constraint")
m.addConstr(5*x1 + 6*x2 <= 500, "oil_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Fried Fish: {x1.x}")
    print(f"Fried Chicken: {x2.x}")
    print(f"Total Revenue: ${4*x1.x + 5*x2.x:.2f}")
else:
    print("No optimal solution found")
```