## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'bowls of pasta' and 'corn cobs', which we can denote as $x_1$ and $x_2$ respectively. The objective function to minimize is $6.74x_1 + 9.12x_2$. The constraints are:
1. $11x_1 + 10x_2 \geq 16$ (carbohydrates constraint)
2. $11x_1 + 10x_2 \leq 54$ (carbohydrates upper bound)
3. $8x_1 - 6x_2 \geq 0$ (linear constraint)
4. $x_1 \geq 0$ and $x_2 \geq 0$ (non-negativity)
5. $x_1$ and $x_2$ are integers (integer constraint)

## 2: Convert the problem into a symbolic representation
The symbolic representation is as follows:
- Variables: $x_1$ for 'bowls of pasta', $x_2$ for 'corn cobs'
- Objective function: $6.74x_1 + 9.12x_2$
- Constraints:
  1. $11x_1 + 10x_2 \geq 16$
  2. $11x_1 + 10x_2 \leq 54$
  3. $8x_1 - 6x_2 \geq 0$
  4. $x_1, x_2 \in \mathbb{Z}^+$

## 3: Express the problem in the required JSON format
```json
{
  'sym_variables': [('x1', 'bowls of pasta'), ('x2', 'corn cobs')],
  'objective_function': '6.74*x1 + 9.12*x2',
  'constraints': [
    '11*x1 + 10*x2 >= 16',
    '11*x1 + 10*x2 <= 54',
    '8*x1 - 6*x2 >= 0',
    'x1, x2 >= 0 and are integers'
  ]
}
```

## 4: Implement the problem using Gurobi
```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="bowls_of_pasta", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="corn_cobs", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(6.74 * x1 + 9.12 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(11 * x1 + 10 * x2 >= 16, name="carbohydrates_min")
    model.addConstr(11 * x1 + 10 * x2 <= 54, name="carbohydrates_max")
    model.addConstr(8 * x1 - 6 * x2 >= 0, name="linear_constraint")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Bowls of pasta: {x1.varValue}")
        print(f"Corn cobs: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```