To solve this optimization problem using Gurobi, we first need to understand and possibly simplify or clarify the given constraints and objective function.

1. **Objective Function**: Minimize \(5x_0 + 2x_1\), where \(x_0\) represents the amount of potatoes and \(x_1\) represents the amount of protein bars.

2. **Constraints**:
    - Healthiness rating: The total healthiness from potatoes and protein bars must be at least 31 but no more than 52. Given that each potato has a healthiness rating of 5 and each protein bar has a rating of 7, we have \(5x_0 + 7x_1 \geq 31\) and \(5x_0 + 7x_1 \leq 52\).
    - Tastiness rating: The total tastiness must be at least 20 but no more than 50. With each potato having a tastiness of 2 and each protein bar having a tastiness of 1, we have \(2x_0 + x_1 \geq 20\) and \(2x_0 + x_1 \leq 50\).
    - Fiber content: At least 24 grams but no more than 30 grams. Given 8 grams per potato and 10 grams per protein bar, we have \(8x_0 + 10x_1 \geq 24\) and \(8x_0 + 10x_1 \leq 30\).
    - Additional constraint: \(9x_0 - x_1 \geq 0\).

3. **Variables**: Both \(x_0\) (potatoes) and \(x_1\) (protein bars) are continuous, meaning they do not have to be whole numbers.

Given these constraints and the objective function, we can model this problem using Gurobi in Python as follows:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="potatoes")
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="protein_bars")

# Objective function: Minimize 5*x0 + 2*x1
m.setObjective(5*x0 + 2*x1, GRB.MINIMIZE)

# Constraints
m.addConstr(5*x0 + 7*x1 >= 31, "healthiness_min")
m.addConstr(5*x0 + 7*x1 <= 52, "healthiness_max")
m.addConstr(2*x0 + x1 >= 20, "tastiness_min")
m.addConstr(2*x0 + x1 <= 50, "tastiness_max")
m.addConstr(8*x0 + 10*x1 >= 24, "fiber_min")
m.addConstr(8*x0 + 10*x1 <= 30, "fiber_max")
m.addConstr(9*x0 - x1 >= 0, "additional_constraint")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Potatoes: {x0.x}")
    print(f"Protein Bars: {x1.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```