## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'eggs', 'strawberries', 'tomatoes', and 'peanutbutter sandwiches', which we can denote 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 $2.65x_0 + 6.12x_1 + 5.16x_2 + 8.03x_3$.

## 3: List the constraints in symbolic notation
The constraints given are:
- $4x_0 + 3x_1 + 12x_2 + 3x_3 \leq 146$ (calcium constraint)
- $6x_0 + 11x_1 + 14x_2 + 14x_3 \leq 90$ (healthiness rating constraint)
- $12x_2 + 3x_3 \geq 13$ (calcium from tomatoes and peanutbutter sandwiches)
- $3x_1 + 12x_2 \geq 31$ (calcium from strawberries and tomatoes)
- $4x_0 + 3x_3 \geq 35$ (calcium from eggs and peanutbutter sandwiches)
- $6x_0 + 11x_1 + 14x_3 \geq 18$ (healthiness from eggs, strawberries, and peanutbutter sandwiches)
- $11x_1 + 14x_2 + 14x_3 \geq 18$ (healthiness from strawberries, tomatoes, and peanutbutter sandwiches)
- $6x_0 + 11x_1 + 14x_2 \geq 18$ (healthiness from eggs, strawberries, and tomatoes)
- $6x_0 + 11x_1 + 14x_3 \geq 13$ (healthiness from eggs, strawberries, and peanutbutter sandwiches)
- $11x_1 + 14x_2 + 14x_3 \geq 13$ (healthiness from strawberries, tomatoes, and peanutbutter sandwiches)
- $6x_0 + 11x_1 + 14x_2 \geq 13$ (healthiness from eggs, strawberries, and tomatoes)
- $12x_2 + 3x_3 \leq 84$ (calcium from tomatoes and peanutbutter sandwiches upper bound)
- $4x_0 + 3x_1 \leq 101$ (calcium from eggs and strawberries)
- $4x_0 + 3x_3 \leq 116$ (calcium from eggs and peanutbutter sandwiches)
- $4x_0 + 12x_2 \leq 47$ (calcium from eggs and tomatoes)
- $3x_1 + 3x_3 \leq 59$ (calcium from strawberries and peanutbutter sandwiches)
- $3x_1 + 12x_2 + 3x_3 \leq 128$ (calcium from strawberries, tomatoes, and peanutbutter sandwiches)
- $4x_0 + 3x_1 + 3x_3 \leq 122$ (calcium from eggs, strawberries, and peanutbutter sandwiches)
- $4x_0 + 12x_2 + 3x_3 \leq 120$ (calcium from eggs, tomatoes, and peanutbutter sandwiches)
- $4x_0 + 3x_1 + 12x_2 + 3x_3 \leq 120$ (total calcium)
- $6x_0 + 14x_3 \leq 69$ (healthiness from eggs and peanutbutter sandwiches)
- $11x_1 + 14x_2 \leq 36$ (healthiness from strawberries and tomatoes)
- $6x_0 + 11x_1 \leq 38$ (healthiness from eggs and strawberries)
- $6x_0 + 11x_1 + 14x_2 + 14x_3 \leq 38$ (total healthiness)

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ['x0', 'eggs'],
        ['x1', 'strawberries'],
        ['x2', 'tomatoes'],
        ['x3', 'peanutbutter sandwiches']
    ],
    'objective_function': '2.65*x0 + 6.12*x1 + 5.16*x2 + 8.03*x3',
    'constraints': [
        '4*x0 + 3*x1 + 12*x2 + 3*x3 <= 146',
        '6*x0 + 11*x1 + 14*x2 + 14*x3 <= 90',
        '12*x2 + 3*x3 >= 13',
        '3*x1 + 12*x2 >= 31',
        '4*x0 + 3*x3 >= 35',
        '6*x0 + 11*x1 + 14*x3 >= 18',
        '11*x1 + 14*x2 + 14*x3 >= 18',
        '6*x0 + 11*x1 + 14*x2 >= 18',
        '6*x0 + 11*x1 + 14*x3 >= 13',
        '11*x1 + 14*x2 + 14*x3 >= 13',
        '6*x0 + 11*x1 + 14*x2 >= 13',
        '12*x2 + 3*x3 <= 84',
        '4*x0 + 3*x1 <= 101',
        '4*x0 + 3*x3 <= 116',
        '4*x0 + 12*x2 <= 47',
        '3*x1 + 3*x3 <= 59',
        '3*x1 + 12*x2 + 3*x3 <= 128',
        '4*x0 + 3*x1 + 3*x3 <= 122',
        '4*x0 + 12*x2 + 3*x3 <= 120',
        '4*x0 + 3*x1 + 12*x2 + 3*x3 <= 120',
        '6*x0 + 14*x3 <= 69',
        '11*x1 + 14*x2 <= 36',
        '6*x0 + 11*x1 <= 38',
        '6*x0 + 11*x1 + 14*x2 + 14*x3 <= 38'
    ]
}
```

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

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    eggs = model.addVar(name="eggs", lb=0)
    strawberries = model.addVar(name="strawberries", lb=0)
    tomatoes = model.addVar(name="tomatoes", lb=0)
    peanutbutter_sandwiches = model.addVar(name="peanutbutter_sandwiches", lb=0)

    # Objective function
    model.setObjective(2.65 * eggs + 6.12 * strawberries + 5.16 * tomatoes + 8.03 * peanutbutter_sandwiches, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(4 * eggs + 3 * strawberries + 12 * tomatoes + 3 * peanutbutter_sandwiches <= 146)
    model.addConstr(6 * eggs + 11 * strawberries + 14 * tomatoes + 14 * peanutbutter_sandwiches <= 90)
    model.addConstr(12 * tomatoes + 3 * peanutbutter_sandwiches >= 13)
    model.addConstr(3 * strawberries + 12 * tomatoes >= 31)
    model.addConstr(4 * eggs + 3 * peanutbutter_sandwiches >= 35)
    model.addConstr(6 * eggs + 11 * strawberries + 14 * peanutbutter_sandwiches >= 18)
    model.addConstr(11 * strawberries + 14 * tomatoes + 14 * peanutbutter_sandwiches >= 18)
    model.addConstr(6 * eggs + 11 * strawberries + 14 * tomatoes >= 18)
    model.addConstr(6 * eggs + 11 * strawberries + 14 * peanutbutter_sandwiches >= 13)
    model.addConstr(11 * strawberries + 14 * tomatoes + 14 * peanutbutter_sandwiches >= 13)
    model.addConstr(6 * eggs + 11 * strawberries + 14 * tomatoes >= 13)
    model.addConstr(12 * tomatoes + 3 * peanutbutter_sandwiches <= 84)
    model.addConstr(4 * eggs + 3 * strawberries <= 101)
    model.addConstr(4 * eggs + 3 * peanutbutter_sandwiches <= 116)
    model.addConstr(4 * eggs + 12 * tomatoes <= 47)
    model.addConstr(3 * strawberries + 3 * peanutbutter_sandwiches <= 59)
    model.addConstr(3 * strawberries + 12 * tomatoes + 3 * peanutbutter_sandwiches <= 128)
    model.addConstr(4 * eggs + 3 * strawberries + 3 * peanutbutter_sandwiches <= 122)
    model.addConstr(4 * eggs + 12 * tomatoes + 3 * peanutbutter_sandwiches <= 120)
    model.addConstr(4 * eggs + 3 * strawberries + 12 * tomatoes + 3 * peanutbutter_sandwiches <= 120)
    model.addConstr(6 * eggs + 14 * peanutbutter_sandwiches <= 69)
    model.addConstr(11 * strawberries + 14 * tomatoes <= 36)
    model.addConstr(6 * eggs + 11 * strawberries <= 38)
    model.addConstr(6 * eggs + 11 * strawberries + 14 * tomatoes + 14 * peanutbutter_sandwiches <= 38)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Eggs: ", eggs.varValue)
        print("Strawberries: ", strawberries.varValue)
        print("Tomatoes: ", tomatoes.varValue)
        print("Peanutbutter sandwiches: ", peanutbutter_sandwiches.varValue)
    else:
        print("No optimal solution found")

solve_optimization_problem()
```