## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'eggs' and 'oranges', which we will denote as $x_1$ and $x_2$ respectively. The objective function to maximize is $1.69x_1 + 5.7x_2$. The constraints are:
- $3x_1 + 11x_2 \geq 25$ (minimum protein)
- $14x_1 + 9x_2 \geq 16$ (minimum sourness index)
- $7x_1 - x_2 \geq 0$ (relationship between eggs and oranges)
- $3x_1 + 11x_2 \leq 55$ (maximum protein)
- $14x_1 + 9x_2 \leq 68$ (maximum sourness index)
- $x_1 \in \mathbb{Z}$ (integer number of eggs)
- $x_2 \in \mathbb{Z}$ (integer number of oranges)

## Step 2: Convert the problem into a Gurobi-compatible format
We need to maximize $1.69x_1 + 5.7x_2$ subject to the given constraints. In Gurobi, this can be represented using the following Python code:

```python
import gurobi as gp

# Define the model
m = gp.Model("optimization_problem")

# Define the variables
x1 = m.addVar(name="eggs", vtype=gp.GRB.INTEGER)  # eggs
x2 = m.addVar(name="oranges", vtype=gp.GRB.INTEGER)  # oranges

# Define the objective function
m.setObjective(1.69 * x1 + 5.7 * x2, gp.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(3 * x1 + 11 * x2 >= 25, name="min_protein")
m.addConstr(14 * x1 + 9 * x2 >= 16, name="min_sourness")
m.addConstr(7 * x1 - x2 >= 0, name="relationship")
m.addConstr(3 * x1 + 11 * x2 <= 55, name="max_protein")
m.addConstr(14 * x1 + 9 * x2 <= 68, name="max_sourness")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Eggs: {x1.varValue}, Oranges: {x2.varValue}")
else:
    print("No optimal solution found.")
```

## 3: Provide the symbolic representation of the problem
The symbolic representation is as follows:
```json
{
    'sym_variables': [('x1', 'eggs'), ('x2', 'oranges')],
    'objective_function': '1.69*x1 + 5.7*x2',
    'constraints': [
        '3*x1 + 11*x2 >= 25',
        '14*x1 + 9*x2 >= 16',
        '7*x1 - x2 >= 0',
        '3*x1 + 11*x2 <= 55',
        '14*x1 + 9*x2 <= 68',
        'x1 ∈ ℤ',
        'x2 ∈ ℤ'
    ]
}
```

The final answer is: 
```python
import gurobi as gp

# Define the model
m = gp.Model("optimization_problem")

# Define the variables
x1 = m.addVar(name="eggs", vtype=gp.GRB.INTEGER)  # eggs
x2 = m.addVar(name="oranges", vtype=gp.GRB.INTEGER)  # oranges

# Define the objective function
m.setObjective(1.69 * x1 + 5.7 * x2, gp.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(3 * x1 + 11 * x2 >= 25, name="min_protein")
m.addConstr(14 * x1 + 9 * x2 >= 16, name="min_sourness")
m.addConstr(7 * x1 - x2 >= 0, name="relationship")
m.addConstr(3 * x1 + 11 * x2 <= 55, name="max_protein")
m.addConstr(14 * x1 + 9 * x2 <= 68, name="max_sourness")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Eggs: {x1.varValue}, Oranges: {x2.varValue}")
else:
    print("No optimal solution found.")
```