To solve the given optimization problem using Gurobi, we need to translate the natural language description into a mathematical model and then implement this model in Python using the Gurobi library.

The objective function to be minimized is: $6 \times \text{potatoes} + 7 \times \text{bananas}$

The constraints given are:
1. Carbohydrates from potatoes and bananas should be at least 39 grams.
2. The total carbohydrates from potatoes and bananas should not exceed 91 grams (as per the 'r0' upper bound).
3. $-5 \times \text{potatoes} + 7 \times \text{bananas} \geq 0$
4. Potatoes must be a non-negative integer.

Let's denote:
- $p$ as the number of potatoes,
- $b$ as the number of bananas.

Given data:
- Each potato contains 2 grams of carbohydrates.
- Each banana contains 12 grams of carbohydrates.

The mathematical formulation based on the given constraints is:
- Minimize: $6p + 7b$
- Subject to:
  - $2p + 12b \geq 39$ (At least 39 grams of carbohydrates)
  - $2p + 12b \leq 91$ (No more than 91 grams of carbohydrates)
  - $-5p + 7b \geq 0$
  - $p \in \mathbb{Z}$, $p \geq 0$ (Non-negative integer amount of potatoes)
  - $b \geq 0$ (Non-negative amount of bananas, can be fractional)

Here's how you could implement this model in Python using Gurobi:

```python
from gurobipy import *

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

# Define variables
potatoes = m.addVar(vtype=GRB.INTEGER, name="potatoes", lb=0)
bananas = m.addVar(vtype=GRB.CONTINUOUS, name="bananas", lb=0)

# Objective function
m.setObjective(6*potatoes + 7*bananas, GRB.MINIMIZE)

# Constraints
m.addConstr(2*potatoes + 12*bananas >= 39, "carb_min")
m.addConstr(2*potatoes + 12*bananas <= 91, "carb_max")
m.addConstr(-5*potatoes + 7*bananas >= 0, "balance")

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Potatoes: {potatoes.x}")
    print(f"Bananas: {bananas.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```