## Step 1: Define the symbolic representation of the variables
The variables are 'bagged salads', 'hamburgers', 'bananas', 'protein bars' which can be represented symbolically as $x_1, x_2, x_3, x_4$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $6.71x_1 + 9.86x_2 + 1.3x_3 + 8.97x_4$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
- $15.89x_3 + 6.29x_4 \geq 65$
- $14.62x_1 + 3.71x_2 \geq 39$
- $3.71x_2 + 6.29x_4 \geq 40$
- $14.62x_1 + 3.71x_2 + 15.89x_3 \geq 44$
- $3.71x_2 + 15.89x_3 + 6.29x_4 \geq 44$
- $14.62x_1 + 3.71x_2 + 15.89x_3 \geq 49$
- $3.71x_2 + 15.89x_3 + 6.29x_4 \geq 49$
- $14.62x_1 + 3.71x_2 + 15.89x_3 + 6.29x_4 \geq 49$
- $5x_1 - 3x_3 + 5x_4 \geq 0$
- $3.71x_2 + 15.89x_3 \leq 197$
- $14.62x_1 + 6.29x_4 \leq 143$
- $14.62x_1 + 15.89x_3 \leq 195$
- $3.71x_2 + 6.29x_4 \leq 285$
- $15.89x_3 + 6.29x_4 \leq 281$
- $14.62x_1 + 3.71x_2 + 6.29x_4 \leq 157$
- $14.62x_1 + 3.71x_2 + 15.89x_3 \leq 306$
- $3.71x_2 + 15.89x_3 + 6.29x_4 \leq 220$

## 4: Represent the problem in JSON format as requested
```json
{
    'sym_variables': [
        ('x1', 'bagged salads'), 
        ('x2', 'hamburgers'), 
        ('x3', 'bananas'), 
        ('x4', 'protein bars')
    ], 
    'objective_function': '6.71*x1 + 9.86*x2 + 1.3*x3 + 8.97*x4', 
    'constraints': [
        '15.89*x3 + 6.29*x4 >= 65',
        '14.62*x1 + 3.71*x2 >= 39',
        '3.71*x2 + 6.29*x4 >= 40',
        '14.62*x1 + 3.71*x2 + 15.89*x3 >= 44',
        '3.71*x2 + 15.89*x3 + 6.29*x4 >= 44',
        '14.62*x1 + 3.71*x2 + 15.89*x3 >= 49',
        '3.71*x2 + 15.89*x3 + 6.29*x4 >= 49',
        '14.62*x1 + 3.71*x2 + 15.89*x3 + 6.29*x4 >= 49',
        '5*x1 - 3*x3 + 5*x4 >= 0',
        '3.71*x2 + 15.89*x3 <= 197',
        '14.62*x1 + 6.29*x4 <= 143',
        '14.62*x1 + 15.89*x3 <= 195',
        '3.71*x2 + 6.29*x4 <= 285',
        '15.89*x3 + 6.29*x4 <= 281',
        '14.62*x1 + 3.71*x2 + 6.29*x4 <= 157',
        '14.62*x1 + 3.71*x2 + 15.89*x3 <= 306',
        '3.71*x2 + 15.89*x3 + 6.29*x4 <= 220'
    ]
}
```

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

def optimize_problem():
    # Create a new Gurobi model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="bagged_salads", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="hamburgers", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="bananas", vtype=gurobi.GRB.INTEGER)
    x4 = model.addVar(name="protein_bars", vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(6.71 * x1 + 9.86 * x2 + 1.3 * x3 + 8.97 * x4, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(15.89 * x3 + 6.29 * x4 >= 65)
    model.addConstr(14.62 * x1 + 3.71 * x2 >= 39)
    model.addConstr(3.71 * x2 + 6.29 * x4 >= 40)
    model.addConstr(14.62 * x1 + 3.71 * x2 + 15.89 * x3 >= 44)
    model.addConstr(3.71 * x2 + 15.89 * x3 + 6.29 * x4 >= 44)
    model.addConstr(14.62 * x1 + 3.71 * x2 + 15.89 * x3 >= 49)
    model.addConstr(3.71 * x2 + 15.89 * x3 + 6.29 * x4 >= 49)
    model.addConstr(14.62 * x1 + 3.71 * x2 + 15.89 * x3 + 6.29 * x4 >= 49)
    model.addConstr(5 * x1 - 3 * x3 + 5 * x4 >= 0)
    model.addConstr(3.71 * x2 + 15.89 * x3 <= 197)
    model.addConstr(14.62 * x1 + 6.29 * x4 <= 143)
    model.addConstr(14.62 * x1 + 15.89 * x3 <= 195)
    model.addConstr(3.71 * x2 + 6.29 * x4 <= 285)
    model.addConstr(15.89 * x3 + 6.29 * x4 <= 281)
    model.addConstr(14.62 * x1 + 3.71 * x2 + 6.29 * x4 <= 157)
    model.addConstr(14.62 * x1 + 3.71 * x2 + 15.89 * x3 <= 306)
    model.addConstr(3.71 * x2 + 15.89 * x3 + 6.29 * x4 <= 220)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("bagged salads: ", x1.varValue)
        print("hamburgers: ", x2.varValue)
        print("bananas: ", x3.varValue)
        print("protein bars: ", x4.varValue)
    else:
        print("The model is infeasible")

optimize_problem()
```