To solve this optimization problem, we will use the Gurobi Python library. The problem involves maximizing an objective function subject to several constraints.

First, let's define the symbolic representation of the problem:

```json
{
  'sym_variables': [
    ('x0', 'apples'), 
    ('x1', 'strips of bacon'), 
    ('x2', 'slices of pizza'), 
    ('x3', 'cornichons')
  ], 
  'objective_function': '9.98*x0 + 3.57*x1 + 3.58*x2 + 8.96*x3', 
  'constraints': [
    '9*x0 + 32*x1 >= 78',
    '3*x1 + 10*x3 >= 39',
    '34*x0 + 17*x2 >= 39',
    '3*x1 + 17*x2 >= 21',
    '35*x2 + 4*x3 <= 310',
    '9*x0 + 32*x1 <= 180',
    '32*x1 + 35*x2 <= 214',
    '9*x0 + 4*x3 <= 201',
    '9*x0 + 35*x2 <= 325',
    '9*x0 + 32*x1 + 35*x2 + 4*x3 <= 325',
    '17*x2 + 10*x3 <= 202',
    '34*x0 + 10*x3 <= 213',
    '3*x1 + 10*x3 <= 175',
    '34*x0 + 3*x1 <= 135',
    '34*x0 + 3*x1 + 17*x2 + 10*x3 <= 135'
  ]
}
```

Now, let's implement the solution using Gurobi Python:

```python
from gurobipy import *

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

# Define the variables
x0 = m.addVar(name="apples", lb=0)
x1 = m.addVar(name="strips_of_bacon", lb=0)
x2 = m.addVar(name="slices_of_pizza", lb=0)
x3 = m.addVar(name="cornichons", lb=0)

# Define the objective function
m.setObjective(9.98*x0 + 3.57*x1 + 3.58*x2 + 8.96*x3, GRB.MAXIMIZE)

# Define the constraints
m.addConstr(9*x0 + 32*x1 >= 78)
m.addConstr(3*x1 + 10*x3 >= 39)
m.addConstr(34*x0 + 17*x2 >= 39)
m.addConstr(3*x1 + 17*x2 >= 21)
m.addConstr(35*x2 + 4*x3 <= 310)
m.addConstr(9*x0 + 32*x1 <= 180)
m.addConstr(32*x1 + 35*x2 <= 214)
m.addConstr(9*x0 + 4*x3 <= 201)
m.addConstr(9*x0 + 35*x2 <= 325)
m.addConstr(9*x0 + 32*x1 + 35*x2 + 4*x3 <= 325)
m.addConstr(17*x2 + 10*x3 <= 202)
m.addConstr(34*x0 + 10*x3 <= 213)
m.addConstr(3*x1 + 10*x3 <= 175)
m.addConstr(34*x0 + 3*x1 <= 135)
m.addConstr(34*x0 + 3*x1 + 17*x2 + 10*x3 <= 135)

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print("Apples:", x0.x)
    print("Strips of bacon:", x1.x)
    print("Slices of pizza:", x2.x)
    print("Cornichons:", x3.x)
else:
    print("No optimal solution found")
```