## Step 1: Define the symbolic representation of the variables
The variables are 'bananas', 'apple pies', 'cherry pies', and 'green beans', which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $4 \cdot bananas + 9 \cdot apple\ pies + 2 \cdot cherry\ pies + 8 \cdot green\ beans$, which in symbolic terms is $4x_0 + 9x_1 + 2x_2 + 8x_3$.

## 3: List the constraints in symbolic notation
1. $10x_0 + 7x_1 + 20x_2 + 9x_3 \leq 169$ (calcium constraint)
2. $2x_0 + 22x_1 + 7x_2 + 6x_3 \leq 212$ (fiber constraint)
3. $7x_1 + 9x_3 \geq 18$ (calcium from apple pies and green beans)
4. $10x_0 + 20x_2 \geq 21$ (calcium from bananas and cherry pies)
5. $20x_2 + 9x_3 \geq 37$ (calcium from cherry pies and green beans)
6. $10x_0 + 20x_2 + 9x_3 \geq 40$ (calcium from bananas, cherry pies, and green beans)
7. $10x_0 + 7x_1 + 20x_2 \geq 40$ (calcium from bananas, apple pies, and cherry pies)
8. $10x_0 + 20x_2 + 9x_3 \geq 33$ (calcium from bananas, cherry pies, and green beans, redundant with 6)
9. $10x_0 + 7x_1 + 20x_2 \geq 33$ (calcium from bananas, apple pies, and cherry pies, redundant with 7)
10. $10x_0 + 7x_1 + 20x_2 + 9x_3 \geq 33$ (calcium from all, redundant with 1)
11. $22x_1 + 6x_3 \geq 33$ (fiber from apple pies and green beans)
12. $2x_0 + 7x_2 \geq 35$ (fiber from bananas and cherry pies)
13. $2x_0 + 22x_1 + 6x_3 \geq 28$ (fiber from bananas, apple pies, and green beans)
14. $2x_0 + 22x_1 + 7x_2 \geq 28$ (fiber from bananas, apple pies, and cherry pies)
15. $2x_0 + 22x_1 + 6x_3 \geq 33$ (fiber from bananas, apple pies, and green beans, redundant with 13)
16. $2x_0 + 22x_1 + 7x_2 \geq 33$ (fiber from bananas, apple pies, and cherry pies, redundant with 14)
17. $2x_0 + 22x_1 + 7x_2 + 6x_3 \geq 33$ (fiber from all, redundant)
18. $-8x_0 + 10x_3 \geq 0$
19. $8x_0 - 2x_1 \geq 0$
20. $-3x_0 + 9x_2 + 4x_3 \geq 0$
21. $10x_0 + 20x_2 + 9x_3 \leq 45$ (calcium from bananas, cherry pies, and green beans)
22. $7x_1 + 20x_2 + 9x_3 \leq 82$ (calcium from apple pies, cherry pies, and green beans)
23. $10x_0 + 7x_1 + 20x_2 \leq 53$ (calcium from bananas, apple pies, and cherry pies)
24. $22x_1 + 6x_3 \leq 122$ (fiber from apple pies and green beans)

## 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'bananas'),
        ('x1', 'apple pies'),
        ('x2', 'cherry pies'),
        ('x3', 'green beans')
    ],
    'objective_function': '4*x0 + 9*x1 + 2*x2 + 8*x3',
    'constraints': [
        '10*x0 + 7*x1 + 20*x2 + 9*x3 <= 169',
        '2*x0 + 22*x1 + 7*x2 + 6*x3 <= 212',
        '7*x1 + 9*x3 >= 18',
        '10*x0 + 20*x2 >= 21',
        '20*x2 + 9*x3 >= 37',
        '10*x0 + 20*x2 + 9*x3 >= 40',
        '10*x0 + 7*x1 + 20*x2 >= 40',
        '-8*x0 + 10*x3 >= 0',
        '8*x0 - 2*x1 >= 0',
        '-3*x0 + 9*x2 + 4*x3 >= 0',
        '10*x0 + 20*x2 + 9*x3 <= 45',
        '7*x1 + 20*x2 + 9*x3 <= 82',
        '10*x0 + 7*x1 + 20*x2 <= 53',
        '22*x1 + 6*x3 <= 122',
        'x2 >= 0', 'x2 == int(x2)'  # cherry pies must be an integer
    ]
}
```

## 5: Write the Gurobi code
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    bananas = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="bananas", vtype=gurobi.GRB.CONTINUOUS)
    apple_pies = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="apple_pies", vtype=gurobi.GRB.CONTINUOUS)
    cherry_pies = model.addVar(lb=0, name="cherry_pies", vtype=gurobi.GRB.INTEGER)
    green_beans = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="green_beans", vtype=gurobi.GRB.CONTINUOUS)

    # Objective function
    model.setObjective(4 * bananas + 9 * apple_pies + 2 * cherry_pies + 8 * green_beans, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(10 * bananas + 7 * apple_pies + 20 * cherry_pies + 9 * green_beans <= 169)
    model.addConstr(2 * bananas + 22 * apple_pies + 7 * cherry_pies + 6 * green_beans <= 212)
    model.addConstr(7 * apple_pies + 9 * green_beans >= 18)
    model.addConstr(10 * bananas + 20 * cherry_pies >= 21)
    model.addConstr(20 * cherry_pies + 9 * green_beans >= 37)
    model.addConstr(10 * bananas + 20 * cherry_pies + 9 * green_beans >= 40)
    model.addConstr(10 * bananas + 7 * apple_pies + 20 * cherry_pies >= 40)
    model.addConstr(-8 * bananas + 10 * green_beans >= 0)
    model.addConstr(8 * bananas - 2 * apple_pies >= 0)
    model.addConstr(-3 * bananas + 9 * cherry_pies + 4 * green_beans >= 0)
    model.addConstr(10 * bananas + 20 * cherry_pies + 9 * green_beans <= 45)
    model.addConstr(7 * apple_pies + 20 * cherry_pies + 9 * green_beans <= 82)
    model.addConstr(10 * bananas + 7 * apple_pies + 20 * cherry_pies <= 53)
    model.addConstr(22 * apple_pies + 6 * green_beans <= 122)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Objective: ", model.objval)
        print("Bananas: ", bananas.varValue)
        print("Apple Pies: ", apple_pies.varValue)
        print("Cherry Pies: ", cherry_pies.varValue)
        print("Green Beans: ", green_beans.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```