To solve this optimization problem using Gurobi, we first need to formulate the problem in a way that Gurobi can understand. This involves defining the variables, the objective function, and all the constraints.

### Problem Formulation

#### Variables
- Let \(x_0\) be the number of black beans,
- \(x_1\) be the number of strawberries,
- \(x_2\) be the number of blueberry pies,
- \(x_3\) be the number of bananas.

#### Objective Function
Maximize: \(3x_0 + 3x_1 + 4x_2 + x_3\)

#### Constraints
1. \(2x_0 + 12x_1 + 8x_2 + 4x_3 \leq 610\) (Total cost not exceeding $610)
2. \(20x_0 + x_1 + 22x_2 + 6x_3 \leq 645\) (Carbohydrates not exceeding 645 grams)
3. \(23x_0 + 6x_1 + 19x_2 + 18x_3 \leq 299\) (Sourness index not exceeding 299)
4. \(8x_2 + 4x_3 \geq 53\) (Minimum spend on blueberry pies and bananas)
5. \(12x_1 + 8x_2 \geq 143\) (Minimum spend on strawberries and blueberry pies)
6. \(2x_0 + 12x_1 \geq 73\) (Minimum spend on black beans and strawberries)
7. \(2x_0 + 8x_2 \geq 109\) (Minimum spend on black beans and blueberry pies)
8. \(2x_0 + 12x_1 + 4x_3 \geq 129\) (Minimum spend on black beans, strawberries, and bananas)
9. \(20x_0 + x_1 + 6x_3 \geq 146\) (Carbohydrates from black beans, strawberries, and bananas)
10. \(20x_0 + 22x_2 + 6x_3 \geq 146\) (Carbohydrates from black beans, blueberry pies, and bananas)
11. \(x_1 + 22x_2 + 6x_3 \geq 146\) (Carbohydrates from strawberries, blueberry pies, and bananas)
12. \(x_1 + 22x_2 + x_3 \geq 84\) (Carbohydrates from strawberries, blueberry pies, and bananas)
13. \(20x_0 + x_1 + x_3 \geq 84\) (Carbohydrates from black beans, strawberries, and bananas)
14. \(20x_0 + 22x_2 + x_3 \geq 84\) (Carbohydrates from black beans, blueberry pies, and bananas)
15. \(x_1 + 22x_2 + 6x_3 \geq 113\) (Carbohydrates from strawberries, blueberry pies, and bananas)
16. \(20x_0 + x_1 + 6x_3 \geq 113\) (Carbohydrates from black beans, strawberries, and bananas)
17. \(20x_0 + 22x_2 + 6x_3 \geq 113\) (Carbohydrates from black beans, blueberry pies, and bananas)
18. \(23x_0 + 6x_1 + 18x_3 \geq 38\) (Sourness index from black beans, strawberries, and bananas)
19. \(-5x_1 + x_2 + x_3 \geq 0\) (Linear constraint)
20. \(2x_0 + 4x_3 \leq 440\) (Spend on black beans and bananas)
21. \(2x_0 + 8x_2 \leq 172\) (Spend on black beans and blueberry pies)
22. \(2x_0 + 12x_1 \leq 291\) (Spend on black beans and strawberries)
23. \(12x_1 + 8x_2 \leq 193\) (Spend on strawberries and blueberry pies)
24. \(2x_0 + 12x_1 + 8x_2 + 4x_3 \leq 193\) (Total spend constraint)
25. \(x_1 + 22x_2 \leq 574\) (Carbohydrates from strawberries and blueberry pies)
26. \(20x_0 + 22x_2 \leq 204\) (Carbohydrates from black beans and blueberry pies)
27. \(22x_2 + 6x_3 \leq 336\) (Carbohydrates from blueberry pies and bananas)
28. \(20x_0 + x_1 \leq 217\) (Carbohydrates from black beans and strawberries)
29. \(20x_0 + 6x_3 \leq 535\) (Carbohydrates from black beans and bananas)
30. \(20x_0 + 22x_2 + 6x_3 \leq 168\) (Carbohydrates constraint)
31. \(20x_0 + x_1 + 6x_3 \leq 523\) (Carbohydrates constraint)
32. \(20x_0 + x_1 + 22x_2 \leq 611\) (Carbohydrates constraint)
33. \(23x_0 + 6x_1 \leq 109\) (Sourness index from black beans and strawberries)
34. \(19x_2 + 18x_3 \leq 80\) (Sourness index from blueberry pies and bananas)
35. \(23x_0 + 6x_1 + 19x_2 + 18x_3 \leq 80\) (Total sourness index)

### Gurobi Code

```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()
    
    # Define variables
    x0 = model.addVar(name="black_beans", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="strawberries", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="blueberry_pies", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="bananas", vtype=gurobi.GRB.INTEGER)
    
    # Objective function: Maximize 3x0 + 3x1 + 4x2 + x3
    model.setObjective(3*x0 + 3*x1 + 4*x2 + x3, gurobi.GRB.MAXIMIZE)
    
    # Constraints
    model.addConstr(2*x0 + 12*x1 + 8*x2 + 4*x3 <= 610)
    model.addConstr(20*x0 + x1 + 22*x2 + 6*x3 <= 645)
    model.addConstr(23*x0 + 6*x1 + 19*x2 + 18*x3 <= 299)
    model.addConstr(8*x2 + 4*x3 >= 53)
    model.addConstr(12*x1 + 8*x2 >= 143)
    model.addConstr(2*x0 + 12*x1 >= 73)
    model.addConstr(2*x0 + 8*x2 >= 109)
    model.addConstr(2*x0 + 12*x1 + 4*x3 >= 129)
    model.addConstr(20*x0 + x1 + 6*x3 >= 146)
    model.addConstr(20*x0 + 22*x2 + 6*x3 >= 146)
    model.addConstr(x1 + 22*x2 + 6*x3 >= 146)
    model.addConstr(x1 + 22*x2 + x3 >= 84)
    model.addConstr(20*x0 + x1 + x3 >= 84)
    model.addConstr(20*x0 + 22*x2 + x3 >= 84)
    model.addConstr(x1 + 22*x2 + 6*x3 >= 113)
    model.addConstr(20*x0 + x1 + 6*x3 >= 113)
    model.addConstr(20*x0 + 22*x2 + 6*x3 >= 113)
    model.addConstr(23*x0 + 6*x1 + 18*x3 >= 38)
    model.addConstr(-5*x1 + x2 + x3 >= 0)
    model.addConstr(2*x0 + 4*x3 <= 440)
    model.addConstr(2*x0 + 8*x2 <= 172)
    model.addConstr(2*x0 + 12*x1 <= 291)
    model.addConstr(12*x1 + 8*x2 <= 193)
    model.addConstr(2*x0 + 12*x1 + 8*x2 + 4*x3 <= 193)
    model.addConstr(x1 + 22*x2 <= 574)
    model.addConstr(20*x0 + 22*x2 <= 204)
    model.addConstr(22*x2 + 6*x3 <= 336)
    model.addConstr(20*x0 + x1 <= 217)
    model.addConstr(20*x0 + 6*x3 <= 535)
    model.addConstr(20*x0 + 22*x2 + 6*x3 <= 168)
    model.addConstr(20*x0 + x1 + 6*x3 <= 523)
    model.addConstr(20*x0 + x1 + 22*x2 <= 611)
    model.addConstr(23*x0 + 6*x1 <= 109)
    model.addConstr(19*x2 + 18*x3 <= 80)
    model.addConstr(23*x0 + 6*x1 + 19*x2 + 18*x3 <= 80)
    
    # Solve the model
    model.optimize()
    
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Black beans: ", x0.varValue)
        print("Strawberries: ", x1.varValue)
        print("Blueberry pies: ", x2.varValue)
        print("Bananas: ", x3.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```