## Step 1: Define the symbolic representation of the variables
The variables are 'kiwis', 'cantaloupes', 'cherry pies', and 'cornichons', which can be represented symbolically as 'x1', 'x2', 'x3', and 'x4' respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $1 \cdot kiwis + 5 \cdot cantaloupes + 7 \cdot cherry\ pies + 7 \cdot cornichons$. In symbolic notation, this becomes $1x_1 + 5x_2 + 7x_3 + 7x_4$.

## 3: Define the constraints in symbolic notation
1. $5x_1 + 20x_2 + 2x_3 + 9x_4 \leq 261$ (carbohydrates constraint)
2. $5x_1 + 9x_4 \geq 59$ (kiwis and cornichons carbohydrates)
3. $20x_2 + 2x_3 \geq 42$ (cantaloupes and cherry pies carbohydrates)
4. $2x_3 + 9x_4 \geq 55$ (cherry pies and cornichons carbohydrates)
5. $5x_1 + 2x_3 \geq 39$ (kiwis and cherry pies carbohydrates)
6. $5x_1 + 20x_2 + 2x_3 + 9x_4 \geq 39$ (all sources carbohydrates)
7. $6x_3 - 3x_4 \geq 0$ (cherry pies and cornichons relationship)
8. $-9x_2 + 2x_3 \geq 0$ (cantaloupes and cherry pies relationship)

## 4: Specify variable bounds and types
- $x_1$ (kiwis) is an integer
- $x_2$ (cantaloupes) is an integer
- $x_3$ (cherry pies) is an integer
- $x_4$ (cornichons) is a continuous variable

## 5: Create the Gurobi model and variables
We will use Gurobi to solve this optimization problem.

```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x1 = m.addVar(name="kiwis", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="cantaloupes", vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name="cherry_pies", vtype=gurobi.GRB.INTEGER)
x4 = m.addVar(name="cornichons")

# Objective function
m.setObjective(x1 + 5 * x2 + 7 * x3 + 7 * x4, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(5 * x1 + 20 * x2 + 2 * x3 + 9 * x4 <= 261, name="carbohydrates")
m.addConstr(5 * x1 + 9 * x4 >= 59, name="kiwis_cornichons")
m.addConstr(20 * x2 + 2 * x3 >= 42, name="cantaloupes_cherry_pies")
m.addConstr(2 * x3 + 9 * x4 >= 55, name="cherry_pies_cornichons")
m.addConstr(5 * x1 + 2 * x3 >= 39, name="kiwis_cherry_pies")
m.addConstr(5 * x1 + 20 * x2 + 2 * x3 + 9 * x4 >= 39, name="all_sources")
m.addConstr(6 * x3 - 3 * x4 >= 0, name="cherry_pies_cornichons_relationship")
m.addConstr(-9 * x2 + 2 * x3 >= 0, name="cantaloupes_cherry_pies_relationship")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Kiwis: ", x1.varValue)
    print("Cantaloupes: ", x2.varValue)
    print("Cherry Pies: ", x3.varValue)
    print("Cornichons: ", x4.varValue)
else:
    print("The model is infeasible")
```

## 6: Symbolic Representation
The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'kiwis'), ('x2', 'cantaloupes'), ('x3', 'cherry pies'), ('x4', 'cornichons')],
    'objective_function': '1*x1 + 5*x2 + 7*x3 + 7*x4',
    'constraints': [
        '5*x1 + 20*x2 + 2*x3 + 9*x4 <= 261',
        '5*x1 + 9*x4 >= 59',
        '20*x2 + 2*x3 >= 42',
        '2*x3 + 9*x4 >= 55',
        '5*x1 + 2*x3 >= 39',
        '5*x1 + 20*x2 + 2*x3 + 9*x4 >= 39',
        '6*x3 - 3*x4 >= 0',
        '-9*x2 + 2*x3 >= 0'
    ]
}
```