To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints.

Let's denote:
- $x_1$ as the quantity of tomatoes,
- $x_2$ as the number of corn cobs.

The objective function to minimize is: $3.97x_1 + 3.18x_2$

Given the resources/attributes:
- Healthiness rating for tomatoes: 0.53, for corn cobs: 2.22
- Grams of fat for tomatoes: 4.2, for corn cobs: 2.22
- Umami index for tomatoes: 0.28, for corn cobs: 4.12

Constraints:
1. Total healthiness rating is at least 7: $0.53x_1 + 2.22x_2 \geq 7$
2. Total grams of fat is at least 19: $4.2x_1 + 2.22x_2 \geq 19$
3. Total umami index is at least 5: $0.28x_1 + 4.12x_2 \geq 5$
4. Constraint on tomatoes and corn cobs: $-7x_1 + x_2 \geq 0$
5. Maximum total healthiness rating is 14: $0.53x_1 + 2.22x_2 \leq 14$
6. Maximum total grams of fat is 47: $4.2x_1 + 2.22x_2 \leq 47$
7. Maximum total umami index is 7: $0.28x_1 + 4.12x_2 \leq 7$

Symbolic representation:
```json
{
    'sym_variables': [('x1', 'tomatoes'), ('x2', 'corn cobs')],
    'objective_function': '3.97*x1 + 3.18*x2',
    'constraints': [
        '0.53*x1 + 2.22*x2 >= 7',
        '4.2*x1 + 2.22*x2 >= 19',
        '0.28*x1 + 4.12*x2 >= 5',
        '-7*x1 + x2 >= 0',
        '0.53*x1 + 2.22*x2 <= 14',
        '4.2*x1 + 2.22*x2 <= 47',
        '0.28*x1 + 4.12*x2 <= 7'
    ]
}
```

Now, let's implement this problem in Gurobi:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables
x1 = m.addVar(name="tomatoes", lb=0)
x2 = m.addVar(name="corn_cobs", lb=0)

# Set the objective function
m.setObjective(3.97*x1 + 3.18*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(0.53*x1 + 2.22*x2 >= 7, name="healthiness_rating_min")
m.addConstr(4.2*x1 + 2.22*x2 >= 19, name="fat_min")
m.addConstr(0.28*x1 + 4.12*x2 >= 5, name="umami_index_min")
m.addConstr(-7*x1 + x2 >= 0, name="tomatoes_corn_cobs_constraint")
m.addConstr(0.53*x1 + 2.22*x2 <= 14, name="healthiness_rating_max")
m.addConstr(4.2*x1 + 2.22*x2 <= 47, name="fat_max")
m.addConstr(0.28*x1 + 4.12*x2 <= 7, name="umami_index_max")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Tomatoes: {x1.x}")
    print(f"Corn Cobs: {x2.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```