To solve Bob's animal feed mixing problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables and the objective function, followed by the constraints.

### Symbolic Representation

Let:
- $x_1$ represent the amount of oats in kilograms,
- $x_2$ represent the amount of sunflower seeds in kilograms.

The objective is to minimize the total cost, which can be represented as:
\[50x_1 + 70x_2\]

The constraints based on the protein and fat requirements are:
1. Protein constraint: $5x_1 + 10x_2 \geq 250$
2. Fat constraint: $16x_1 + 22x_2 \geq 400$

Additionally, since we cannot have negative amounts of oats or sunflower seeds, we also have:
3. Non-negativity constraints: $x_1 \geq 0$, $x_2 \geq 0$

### Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'oats'), ('x2', 'sunflower seeds')],
    'objective_function': '50*x1 + 70*x2',
    'constraints': ['5*x1 + 10*x2 >= 250', '16*x1 + 22*x2 >= 400', 'x1 >= 0', 'x2 >= 0']
}
```

### Gurobi Code in Python

To solve this linear programming problem using Gurobi, we can write the following Python code:

```python
from gurobipy import *

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

# Add variables
x1 = m.addVar(lb=0, name="oats")
x2 = m.addVar(lb=0, name="sunflower_seeds")

# Set the objective function
m.setObjective(50*x1 + 70*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(5*x1 + 10*x2 >= 250, "protein_constraint")
m.addConstr(16*x1 + 22*x2 >= 400, "fat_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Oats: {x1.x} kg")
    print(f"Sunflower seeds: {x2.x} kg")
    print(f"Total cost: ${m.objVal}")
else:
    print("No optimal solution found")
```