To solve this problem, we first need to define the variables, objective function, and constraints in a symbolic representation.

### Symbolic Representation

```json
{
    'sym_variables': [
        ('x0', 'apple pies'), ('x1', 'bowls of pasta'), ('x2', 'hamburgers'), 
        ('x3', 'chicken thighs'), ('x4', 'steaks'), ('x5', 'protein bars')
    ],
    'objective_function': '5.19*x0 + 9.84*x1 + 8.7*x2 + 2.51*x3 + 2.46*x4 + 3.47*x5',
    'constraints': [
        '2*x0 + 1*x1 + 10*x2 + 2*x3 + 3*x4 + 11*x5 <= 619',
        '7*x0 + 11*x1 + 13*x2 + 3*x3 + 10*x4 + 1*x5 <= 412',
        '2*x0 + 1*x1 <= 619', '7*x0 + 11*x1 <= 412', '10*x2 <= 619', '13*x2 <= 412',
        '2*x3 <= 619', '3*x3 <= 412', '3*x4 <= 619', '10*x4 <= 412', '11*x5 <= 619', '1*x5 <= 412',
        '2*x0 + 2*x3 + 11*x5 >= 93', '10*x2 + 2*x3 + 11*x5 >= 93', '2*x3 + 3*x4 + 11*x5 >= 93',
        '2*x0 + 10*x2 + 11*x5 >= 93', '1*x1 + 2*x3 + 11*x5 >= 93', '10*x2 + 3*x4 >= 93',
        '10*x2 + 3*x4 + 11*x5 >= 93', '2*x0 + 1*x1 + 10*x2 >= 93', '1*x1 + 10*x2 + 11*x5 >= 93',
        '2*x0 + 2*x3 + 11*x5 >= 100', '10*x2 + 2*x3 + 11*x5 >= 100', '2*x3 + 3*x4 + 11*x5 >= 100',
        '2*x0 + 10*x2 + 11*x5 >= 100', '1*x1 + 2*x3 + 11*x5 >= 100', '10*x2 + 3*x4 >= 100',
        '10*x2 + 3*x4 + 11*x5 >= 100', '2*x0 + 1*x1 + 10*x2 >= 100', '1*x1 + 10*x2 + 11*x5 >= 100',
        '2*x0 + 2*x3 + 11*x5 >= 51', '10*x2 + 2*x3 + 11*x5 >= 51', '2*x3 + 3*x4 + 11*x5 >= 51',
        '2*x0 + 10*x2 + 11*x5 >= 51', '1*x1 + 2*x3 + 11*x5 >= 51', '10*x2 + 3*x4 >= 51',
        '10*x2 + 3*x4 + 11*x5 >= 51', '2*x0 + 1*x1 + 10*x2 >= 51', '1*x1 + 10*x2 + 11*x5 >= 51',
        '7*x0 + 11*x1 >= 59', '13*x2 + 3*x4 >= 55', '7*x0 + 13*x2 >= 57',
        '10*x4 + 1*x5 >= 60', '11*x1 + 13*x2 >= 63', '3*x3 + 1*x5 >= 24',
        '13*x2 + 3*x3 >= 46', '7*x0 + 3*x4 >= 45', '11*x1 + 3*x4 + 1*x5 >= 65',
        '7*x0 + 3*x3 + 3*x4 >= 65', '11*x1 + 3*x3 + 1*x5 >= 65', '13*x2 + 3*x4 + 1*x5 >= 65',
        '7*x0 + 13*x2 + 3*x3 >= 65', '11*x1 + 13*x2 + 3*x3 >= 65', '11*x1 + 3*x4 + 1*x5 >= 68',
        '7*x0 + 3*x3 + 3*x4 >= 68', '11*x1 + 3*x3 + 1*x5 >= 68', '13*x2 + 3*x4 + 1*x5 >= 68',
        '7*x0 + 13*x2 + 3*x3 >= 68', '11*x1 + 13*x2 + 3*x3 >= 68', '11*x1 + 3*x4 + 1*x5 >= 40',
        '7*x0 + 3*x3 + 3*x4 >= 40', '11*x1 + 3*x3 + 1*x5 >= 40', '13*x2 + 3*x4 + 1*x5 >= 40',
        '7*x0 + 13*x2 + 3*x3 >= 40', '11*x1 + 13*x2 + 3*x3 >= 40', '11*x1 + 3*x4 + 3*x3 >= 40',
        '11*x1 + 13*x2 + 3*x3 >= 40', '11*x1 + 3*x4 + 1*x5 >= 67',
        '7*x0 + 3*x3 + 3*x4 >= 67', '11*x1 + 3*x3 + 1*x5 >= 67', '13*x2 + 3*x4 + 1*x5 >= 67',
        '7*x0 + 13*x2 + 3*x3 >= 67', '11*x1 + 13*x2 + 3*x3 >= 67', '11*x1 + 3*x4 + 3*x3 >= 67',
        '11*x1 + 13*x2 + 3*x3 >= 67', '11*x1 + 3*x4 + 1*x5 >= 63',
        '7*x0 + 3*x3 + 3*x4 >= 63', '11*x1 + 3*x3 + 1*x5 >= 63', '13*x2 + 3*x4 + 1*x5 >= 63',
        '7*x0 + 13*x2 + 3*x3 >= 63', '11*x1 + 13*x2 + 3*x3 >= 63', '11*x1 + 3*x4 + 3*x3 >= 63',
        '11*x1 + 13*x2 + 3*x3 >= 63', '11*x1 + 3*x4 + 1*x5 >= 46',
        '7*x0 + 3*x3 + 3*x4 >= 46', '11*x1 + 3*x3 + 1*x5 >= 46', '13*x2 + 3*x4 + 1*x5 >= 46',
        '7*x0 + 13*x2 + 3*x3 >= 46', '11*x1 + 13*x2 + 3*x3 >= 46', '1*x1 + 3*x4 <= 410',
        '3*x4 + 1*x5 <= 111', '3*x3 + 1*x5 <= 84', '7*x0 + 1*x5 <= 167',
        '7*x0 + 11*x1 <= 128', '7*x0 + 3*x3 <= 407', '11*x1 + 13*x2 <= 134',
        '13*x2 + 3*x4 <= 223', '7*x0 + 13*x2 <= 274', '13*x2 + 3*x3 <= 204',
        '3*x3 + 3*x4 <= 80', '11*x1 + 3*x3 <= 257', '7*x0 + 3*x4 <= 80',
        '3*x3 + 3*x4 + 1*x5 <= 335', '7*x0 + 11*x1 + 13*x2 <= 128',
        '7*x0 + 11*x1 + 13*x2 + 3*x3 + 3*x4 + 1*x5 <= 128',
        '10*x2 + 1*x1 + 11*x5 <= 550', '2*x3 + 11*x5 <= 367',
        '1*x1 + 11*x5 <= 523', '10*x2 + 2*x3 <= 594',
        '1*x1 + 2*x3 <= 273', '10*x2 + 2*x3 + 11*x5 <= 277',
        '2*x3 + 3*x4 + 11*x5 <= 350', '1*x1 + 10*x2 + 2*x3 <= 263',
        '2*x0 + 10*x2 + 11*x5 <= 181', '2*x0 + 2*x3 + 3*x4 <= 329',
        '2*x0 + 1*x1 + 2*x3 <= 366', '1*x1 + 2*x3 + 3*x4 <= 161',
        '2*x0 + 1*x1 + 11*x5 <= 338', '1*x1 + 3*x4 + 11*x5 <= 184',
        '10*x2 + 3*x4 + 11*x5 <= 277', '2*x0 + 1*x1 + 10*x2 + 2*x3 + 3*x4 + 11*x5 <= 277'
    ]
}
```

### Gurobi Code

```python
import gurobi

def solve_optimization_problem():
    # Define the model
    model = gurobi.Model()

    # Define the variables
    x0 = model.addVar(name="apple_pies", lb=0)
    x1 = model.addVar(name="bowls_of_pasta", lb=0)
    x2 = model.addVar(name="hamburgers", lb=0)
    x3 = model.addVar(name="chicken_thighs", lb=0)
    x4 = model.addVar(name="steaks", lb=0)
    x5 = model.addVar(name="protein_bars", lb=0)

    # Define the objective function
    model.setObjective(5.19*x0 + 9.84*x1 + 8.7*x2 + 2.51*x3 + 2.46*x4 + 3.47*x5, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(2*x0 + 1*x1 + 10*x2 + 2*x3 + 3*x4 + 11*x5 <= 619)
    model.addConstr(7*x0 + 11*x1 + 13*x2 + 3*x3 + 10*x4 + 1*x5 <= 412)
    model.addConstr(2*x0 + 1*x1 <= 619)
    model.addConstr(7*x0 + 11*x1 <= 412)
    model.addConstr(10*x2 <= 619)
    model.addConstr(13*x2 <= 412)
    model.addConstr(2*x3 <= 619)
    model.addConstr(3*x3 <= 412)
    model.addConstr(3*x4 <= 619)
    model.addConstr(10*x4 <= 412)
    model.addConstr(11*x5 <= 619)
    model.addConstr(1*x5 <= 412)

    model.addConstr(2*x0 + 2*x3 + 11*x5 >= 93)
    model.addConstr(10*x2 + 2*x3 + 11*x5 >= 93)
    model.addConstr(2*x3 + 3*x4 + 11*x5 >= 93)
    model.addConstr(2*x0 + 10*x2 + 11*x5 >= 93)
    model.addConstr(1*x1 + 2*x3 + 11*x5 >= 93)
    model.addConstr(10*x2 + 3*x4 >= 93)
    model.addConstr(10*x2 + 3*x4 + 11*x5 >= 93)
    model.addConstr(2*x0 + 1*x1 + 10*x2 >= 93)
    model.addConstr(1*x1 + 10*x2 + 11*x5 >= 93)

    model.addConstr(7*x0 + 11*x1 >= 59)
    model.addConstr(13*x2 + 3*x4 >= 55)
    model.addConstr(7*x0 + 13*x2 >= 57)
    model.addConstr(10*x4 + 1*x5 >= 60)
    model.addConstr(11*x1 + 13*x2 >= 63)
    model.addConstr(3*x3 + 1*x5 >= 24)
    model.addConstr(13*x2 + 3*x3 >= 46)
    model.addConstr(7*x0 + 3*x4 >= 45)
    model.addConstr(11*x1 + 3*x4 + 1*x5 >= 65)

    model.addConstr(1*x1 + 3*x4 <= 410)
    model.addConstr(3*x4 + 1*x5 <= 111)
    model.addConstr(3*x3 + 1*x5 <= 84)
    model.addConstr(7*x0 + 1*x5 <= 167)
    model.addConstr(7*x0 + 11*x1 <= 128)

    model.addConstr(10*x2 + 1*x1 + 11*x5 <= 550)
    model.addConstr(2*x3 + 11*x5 <= 367)
    model.addConstr(1*x1 + 11*x5 <= 523)
    model.addConstr(10*x2 + 2*x3 <= 594)
    model.addConstr(1*x1 + 2*x3 <= 273)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Apple Pies: ", x0.x)
        print("Bowls of Pasta: ", x1.x)
        print("Hamburgers: ", x2.x)
        print("Chicken Thighs: ", x3.x)
        print("Steaks: ", x4.x)
        print("Protein Bars: ", x5.x)
    else:
        print("No optimal solution found")

solve_optimization_problem()
```