To solve the optimization problem described, we need to minimize the objective function that is defined as 8 times the quantity of oranges added to 8 times the quantity of cheeseburgers. The constraints given include limits on the total combined umami index and grams of protein from both oranges and cheeseburgers, as well as a specific linear constraint involving the quantities of oranges and cheeseburgers.

Given the variables:
- Oranges (x0)
- Cheeseburgers (x1)

And the resources/attributes with their respective bounds:
- Umami index: upper bound of 64, but specific constraints are given for minimum and maximum total umami index.
- Grams of protein: upper bound of 207, but again, specific constraints for minimum and maximum total grams of protein are provided.

The objective function to minimize is: 8x0 + 8x1

Constraints:
1. Total combined umami index ≥ 20
2. Total combined umami index ≤ 34
3. Total combined grams of protein ≥ 46
4. Total combined grams of protein ≤ 156
5. 2x0 - 3x1 ≥ 0
6. x0 must be an integer (whole number of oranges)
7. x1 can be a non-integer (fractional number of cheeseburgers is allowed)

Here's the reasoning translated into Gurobi code:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="oranges")  # Whole number of oranges
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="cheeseburgers")  # Non-integer amount of cheeseburgers

# Objective function: Minimize 8 times the quantity of oranges plus 8 times the quantity of cheeseburgers
m.setObjective(8*x0 + 8*x1, GRB.MINIMIZE)

# Constraints
# Total combined umami index >= 20
m.addConstr(10.8*x0 + 3.74*x1 >= 20, name="umami_min")

# Total combined umami index <= 34
m.addConstr(10.8*x0 + 3.74*x1 <= 34, name="umami_max")

# Total combined grams of protein >= 46
m.addConstr(7.17*x0 + 0.2*x1 >= 46, name="protein_min")

# Total combined grams of protein <= 156
m.addConstr(7.17*x0 + 0.2*x1 <= 156, name="protein_max")

# Linear constraint: 2x0 - 3x1 >= 0
m.addConstr(2*x0 - 3*x1 >= 0, name="linear_constraint")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print("Oranges:", x0.x)
    print("Cheeseburgers:", x1.x)
    print("Objective function value:", m.objVal)
else:
    print("No optimal solution found. Status:", m.status)

```