## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'cheeseburgers', 'ham sandwiches', 'blueberry pies', and 'corn cobs', which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $4.45x_0 + 7.62x_1 + 3.95x_2 + 6.3x_3$.

## 3: List the constraints in symbolic notation
The constraints are:
1. $3x_2 + x_1 \geq 39$ (At least 39 grams of carbohydrates must come from ham sandwiches plus blueberry pies)
2. $6x_0 + 13x_3 \geq 59$ (At least 59 grams of carbohydrates from cheeseburgers and corn cobs)
3. $12x_2 + 8x_3 \geq 70$ (Total healthiness rating from blueberry pies and corn cobs must be 70 or more)
4. $x_0 + 12x_2 \geq 40$ (Total healthiness rating from cheeseburgers and blueberry pies must be 40 or more)
5. $5x_1 + 8x_3 \geq 72$ (Total healthiness rating from ham sandwiches and corn cobs must be 72 or more)
6. $5x_1 + 12x_2 \geq 27$ (Total healthiness rating from ham sandwiches and blueberry pies must be 27 or more)
7. $-7x_0 + 2x_1 + 6x_2 \geq 0$ (Linear constraint)
8. $3x_1 + 14x_2 \leq 122$ (At most 122 grams of carbohydrates from ham sandwiches and blueberry pies)
9. $14x_2 + 13x_3 \leq 145$ (At most 145 grams of carbohydrates from blueberry pies and corn cobs)
10. $3x_1 + 13x_3 \leq 205$ (At most 205 grams of carbohydrates from ham sandwiches and corn cobs)
11. $6x_0 + 13x_3 \leq 76$ (At most 76 grams of carbohydrates from cheeseburgers and corn cobs)
12. $6x_0 + 14x_2 \leq 241$ (At most 241 grams of carbohydrates from cheeseburgers and blueberry pies)
13. $6x_0 + 3x_1 \leq 144$ (At most 144 grams of carbohydrates from cheeseburgers and ham sandwiches)
14. $6x_0 + 3x_1 + 14x_2 + 13x_3 \leq 144$ (At most 144 grams of carbohydrates in total from all)
15. $x_0 + 8x_3 \leq 169$ (Total healthiness rating from cheeseburgers and corn cobs must be no more than 169)
16. $x_0 + 5x_1 \leq 272$ (Total healthiness rating from cheeseburgers and ham sandwiches must be no more than 272)
17. $12x_2 + 8x_3 \leq 209$ (Total healthiness rating from blueberry pies and corn cobs must be no more than 209)
18. $5x_1 + 12x_2 \leq 101$ (Total healthiness rating from ham sandwiches and blueberry pies must be no more than 101)
19. $x_0 + 5x_1 + 8x_3 \leq 135$ (Total healthiness rating from cheeseburgers, ham sandwiches, and corn cobs must be no more than 135)
20. $x_0 + 5x_1 + 12x_2 + 8x_3 \leq 135$ (Total healthiness rating from all must be no more than 135)

## 4: Define the symbolic variables and constraints for output
```json
{
'sym_variables': [
    ('x0', 'cheeseburgers'),
    ('x1', 'ham sandwiches'),
    ('x2', 'blueberry pies'),
    ('x3', 'corn cobs')
],
'objective_function': '4.45x0 + 7.62x1 + 3.95x2 + 6.3x3',
'constraints': [
    '3x1 + 14x2 >= 39',
    '6x0 + 13x3 >= 59',
    '12x2 + 8x3 >= 70',
    'x0 + 12x2 >= 40',
    '5x1 + 8x3 >= 72',
    '5x1 + 12x2 >= 27',
    '-7x0 + 2x1 + 6x2 >= 0',
    '3x1 + 14x2 <= 122',
    '14x2 + 13x3 <= 145',
    '3x1 + 13x3 <= 205',
    '6x0 + 13x3 <= 76',
    '6x0 + 14x2 <= 241',
    '6x0 + 3x1 <= 144',
    '6x0 + 3x1 + 14x2 + 13x3 <= 144',
    'x0 + 8x3 <= 169',
    'x0 + 5x1 <= 272',
    '12x2 + 8x3 <= 209',
    '5x1 + 12x2 <= 101',
    'x0 + 5x1 + 8x3 <= 135',
    'x0 + 5x1 + 12x2 + 8x3 <= 135'
]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi

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

# Define the variables
x0 = model.addVar(name="cheeseburgers", lb=0)
x1 = model.addVar(name="ham sandwiches", lb=0)
x2 = model.addVar(name="blueberry pies", lb=0)
x3 = model.addVar(name="corn cobs", lb=0)

# Define the objective function
model.setObjective(4.45 * x0 + 7.62 * x1 + 3.95 * x2 + 6.3 * x3, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(3 * x1 + 14 * x2 >= 39)
model.addConstr(6 * x0 + 13 * x3 >= 59)
model.addConstr(12 * x2 + 8 * x3 >= 70)
model.addConstr(x0 + 12 * x2 >= 40)
model.addConstr(5 * x1 + 8 * x3 >= 72)
model.addConstr(5 * x1 + 12 * x2 >= 27)
model.addConstr(-7 * x0 + 2 * x1 + 6 * x2 >= 0)
model.addConstr(3 * x1 + 14 * x2 <= 122)
model.addConstr(14 * x2 + 13 * x3 <= 145)
model.addConstr(3 * x1 + 13 * x3 <= 205)
model.addConstr(6 * x0 + 13 * x3 <= 76)
model.addConstr(6 * x0 + 14 * x2 <= 241)
model.addConstr(6 * x0 + 3 * x1 <= 144)
model.addConstr(6 * x0 + 3 * x1 + 14 * x2 + 13 * x3 <= 144)
model.addConstr(x0 + 8 * x3 <= 169)
model.addConstr(x0 + 5 * x1 <= 272)
model.addConstr(12 * x2 + 8 * x3 <= 209)
model.addConstr(5 * x1 + 12 * x2 <= 101)
model.addConstr(x0 + 5 * x1 + 8 * x3 <= 135)
model.addConstr(x0 + 5 * x1 + 12 * x2 + 8 * x3 <= 135)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Cheeseburgers: ", x0.varValue)
    print("Ham sandwiches: ", x1.varValue)
    print("Blueberry pies: ", x2.varValue)
    print("Corn cobs: ", x3.varValue)
else:
    print("The model is infeasible")
```