To tackle the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables for each item (eggs and hot dogs), formulating the objective function using these variables, and then listing out all constraints in terms of these variables.

Let's denote:
- \(x_1\) as the quantity of eggs,
- \(x_2\) as the quantity of hot dogs.

The objective function is to maximize \(5.97x_1 + 9.26x_2\).

Given constraints:
1. Fiber constraint: \(7x_1 + 6x_2 \leq 53\) (upper bound of fiber),
2. Sourness index constraint: \(x_1 + 9x_2 \leq 25\) (upper bound of sourness index),
3. Minimum fiber requirement: \(7x_1 + 6x_2 \geq 12\),
4. Minimum sourness index requirement: \(x_1 + 9x_2 \geq 4\),
5. Linear constraint: \(-3x_1 + 2x_2 \geq 0\),
6. Fiber upper bound (repeated but with a value of 26): \(7x_1 + 6x_2 \leq 26\),
7. Sourness index upper bound (repeated with the same value): \(x_1 + 9x_2 \leq 21\).

The symbolic representation is thus:
```json
{
    'sym_variables': [('x1', 'eggs'), ('x2', 'hot dogs')],
    'objective_function': '5.97*x1 + 9.26*x2',
    'constraints': [
        '7*x1 + 6*x2 <= 53', 
        'x1 + 9*x2 <= 25', 
        '7*x1 + 6*x2 >= 12', 
        'x1 + 9*x2 >= 4', 
        '-3*x1 + 2*x2 >= 0', 
        '7*x1 + 6*x2 <= 26', 
        'x1 + 9*x2 <= 21'
    ]
}
```

Now, let's implement this problem in Gurobi Python:

```python
from gurobipy import *

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

# Add variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="eggs")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="hot_dogs")

# Set the objective function
m.setObjective(5.97*x1 + 9.26*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(7*x1 + 6*x2 <= 53, "fiber_upper_bound")
m.addConstr(x1 + 9*x2 <= 25, "sourness_index_upper_bound")
m.addConstr(7*x1 + 6*x2 >= 12, "minimum_fiber_requirement")
m.addConstr(x1 + 9*x2 >= 4, "minimum_sourness_index_requirement")
m.addConstr(-3*x1 + 2*x2 >= 0, "linear_constraint")
m.addConstr(7*x1 + 6*x2 <= 26, "fiber_upper_bound_26")
m.addConstr(x1 + 9*x2 <= 21, "sourness_index_upper_bound_21")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Eggs: {x1.x}, Hot Dogs: {x2.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```