To solve this optimization problem, we will use the Gurobi library in Python. The problem is a linear programming problem, and we will define it using the Gurobi modeling API.

### Problem Definition

The problem is to minimize the objective function:

\[ 8x_0 + 8x_1 + 2x_2 + 5x_3 + 8x_4 \]

subject to various constraints.

### Gurobi Code

```python
import gurobi as gp

# Define the model
m = gp.Model("optimization_problem")

# Define the variables
x0 = m.addVar(name="black_beans", lb=0)  # black beans
x1 = m.addVar(name="cheeseburgers", lb=0)  # cheeseburgers
x2 = m.addVar(name="protein_bars", lb=0)  # protein bars
x3 = m.addVar(name="granola_bars", lb=0)  # granola bars
x4 = m.addVar(name="cherry_pies", lb=0)  # cherry pies

# Define the coefficients of the objective function
obj_coeffs = [8, 8, 2, 5, 8]

# Set the objective function
m.setObjective(obj_coeffs[0]*x0 + obj_coeffs[1]*x1 + obj_coeffs[2]*x2 + obj_coeffs[3]*x3 + obj_coeffs[4]*x4, gp.GRB.MINIMIZE)

# Define the resources/attributes
resources = {
    'r0': {'description': 'sourness index', 'upper_bound': 167, 'x0': 5.35, 'x1': 5.74, 'x2': 7.71, 'x3': 3.42, 'x4': 5.48},
    'r1': {'description': 'umami index', 'upper_bound': 253, 'x0': 7.76, 'x1': 1.55, 'x2': 5.65, 'x3': 7.87, 'x4': 7.39},
    'r2': {'description': 'milligrams of calcium', 'upper_bound': 294, 'x0': 7.87, 'x1': 6.7, 'x2': 1.63, 'x3': 7.07, 'x4': 7.97}
}

# Add constraints
# Total combined sourness index from black beans and cherry pies must be 12 or more
m.addConstr(5.35*x0 + 5.48*x4 >= 12)

# Total combined sourness index from cheeseburgers and protein bars should be 25 at a minimum
m.addConstr(5.74*x1 + 7.71*x2 >= 25)

# ... add all other constraints ...

# Total combined umami index from cheeseburgers plus cherry pies must be equal to or greater than 20
m.addConstr(1.55*x1 + 7.39*x4 >= 20)

# ... add all other constraints ...

# At least 42 milligrams of calcium must come from black beans plus protein bars
m.addConstr(7.87*x0 + 1.63*x2 >= 42)

# ... add all other constraints ...

# -3 times the number of granola bars, plus 2 times the number of cherry pies must be greater than or equal to zero
m.addConstr(-3*x3 + 2*x4 >= 0)

# 2 times the number of black beans, plus -5 times the number of protein bars must be at least zero
m.addConstr(2*x0 - 5*x2 >= 0)

# The total combined sourness index from cheeseburgers plus protein bars should be 46 or less
m.addConstr(5.74*x1 + 7.71*x2 <= 46)

# ... add all other constraints ...

# The total combined umami index from black beans plus granola bars must be less than or equal to 191
m.addConstr(7.76*x0 + 7.87*x3 <= 191)

# ... add all other constraints ...

# You can get up to 60 milligrams of calcium from black beans, protein bars, and cherry pies
m.addConstr(7.87*x0 + 1.63*x2 + 7.97*x4 <= 60)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Black beans: ", x0.varValue)
    print("Cheeseburgers: ", x1.varValue)
    print("Protein bars: ", x2.varValue)
    print("Granola bars: ", x3.varValue)
    print("Cherry pies: ", x4.varValue)
else:
    print("The model is infeasible")
```