To solve the given optimization problem using Gurobi, we first need to understand and possibly simplify or clarify the constraints provided. The objective function to minimize is: $3.97 \times \text{tomatoes} + 3.18 \times \text{corn cobs}$.

Given resources/attributes are:
- 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 $\geq 7$
2. Total grams of fat $\geq 19$
3. Total umami index $\geq 5$
4. $-7 \times \text{tomatoes} + 1 \times \text{corn cobs} \geq 0$
5. Total healthiness rating $\leq 14$
6. Total grams of fat $\leq 47$
7. Total umami index $\leq 7$

Let's denote the number of tomatoes as $x_0$ and the number of corn cobs as $x_1$. The problem can be formulated as a linear programming problem.

The objective function is: $\min 3.97x_0 + 3.18x_1$

Subject to:
- $0.53x_0 + 2.22x_1 \geq 7$ (Total healthiness rating)
- $4.2x_0 + 2.22x_1 \geq 19$ (Total grams of fat)
- $0.28x_0 + 4.12x_1 \geq 5$ (Total umami index)
- $-7x_0 + x_1 \geq 0$
- $0.53x_0 + 2.22x_1 \leq 14$ (Total healthiness rating upper bound)
- $4.2x_0 + 2.22x_1 \leq 47$ (Total grams of fat upper bound)
- $0.28x_0 + 4.12x_1 \leq 7$ (Total umami index upper bound)

Since both variables are allowed to be non-integer, we don't need to specify integer constraints for them.

Here is how you can implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Add variables
x0 = m.addVar(lb=0, name="tomatoes")  # Number of tomatoes
x1 = m.addVar(lb=0, name="corn_cobs")  # Number of corn cobs

# Set the objective function
m.setObjective(3.97*x0 + 3.18*x1, GRB.MINIMIZE)

# Add constraints
m.addConstr(0.53*x0 + 2.22*x1 >= 7, name="healthiness_rating_lower")
m.addConstr(4.2*x0 + 2.22*x1 >= 19, name="fat_grams_lower")
m.addConstr(0.28*x0 + 4.12*x1 >= 5, name="umami_index_lower")
m.addConstr(-7*x0 + x1 >= 0, name="mixed_constraint")
m.addConstr(0.53*x0 + 2.22*x1 <= 14, name="healthiness_rating_upper")
m.addConstr(4.2*x0 + 2.22*x1 <= 47, name="fat_grams_upper")
m.addConstr(0.28*x0 + 4.12*x1 <= 7, name="umami_index_upper")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Tomatoes: {x0.x}, Corn Cobs: {x1.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```