## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'tomatoes' and 'corn cobs', which we can represent symbolically as $x_0$ and $x_1$ respectively. The objective function to minimize is $3.97x_0 + 3.18x_1$. The constraints are:
- $0.53x_0 + 2.22x_1 \geq 7$
- $4.2x_0 + 2.22x_1 \geq 19$
- $0.28x_0 + 4.12x_1 \geq 5$
- $-7x_0 + x_1 \geq 0$
- $0.53x_0 + 2.22x_1 \leq 14$
- $4.2x_0 + 2.22x_1 \leq 47$
- $0.28x_0 + 4.12x_1 \leq 7$

## Step 2: Convert the problem into a Gurobi-compatible format
We need to define the variables, the objective function, and the constraints in a way that Gurobi can understand.

## 3: Write the Gurobi code
```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(name="tomatoes", lb=0)  # tomatoes
x1 = model.addVar(name="corn_cobs", lb=0)  # corn cobs

# Define the objective function
model.setObjective(3.97 * x0 + 3.18 * x1, gurobi.GRB.MINIMIZE)

# Define the constraints
model.addConstr(0.53 * x0 + 2.22 * x1 >= 7, name="healthiness_rating_min")
model.addConstr(4.2 * x0 + 2.22 * x1 >= 19, name="grams_of_fat_min")
model.addConstr(0.28 * x0 + 4.12 * x1 >= 5, name="umami_index_min")
model.addConstr(-7 * x0 + x1 >= 0, name="tomatoes_corn_cobs_ratio")
model.addConstr(0.53 * x0 + 2.22 * x1 <= 14, name="healthiness_rating_max")
model.addConstr(4.2 * x0 + 2.22 * x1 <= 47, name="grams_of_fat_max")
model.addConstr(0.28 * x0 + 4.12 * x1 <= 7, name="umami_index_max")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Tomatoes: {x0.varValue}")
    print(f"Corn Cobs: {x1.varValue}")
    print(f"Objective Function: {model.objVal}")
else:
    print("No optimal solution found.")
```

## 4: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'tomatoes'), ('x1', 'corn cobs')],
    'objective_function': '3.97*x0 + 3.18*x1',
    'constraints': [
        '0.53*x0 + 2.22*x1 >= 7',
        '4.2*x0 + 2.22*x1 >= 19',
        '0.28*x0 + 4.12*x1 >= 5',
        '-7*x0 + x1 >= 0',
        '0.53*x0 + 2.22*x1 <= 14',
        '4.2*x0 + 2.22*x1 <= 47',
        '0.28*x0 + 4.12*x1 <= 7'
    ]
}
```