## Step 1: Define the symbolic representation of the problem
First, let's define the symbolic variables and their corresponding natural language objects:
- $x_0$ represents 'cartons of milk'
- $x_1$ represents 'packs of napkins'
- $x_2$ represents 'paper towel rolls'
- $x_3$ represents 'cookies'

## Step 2: Formulate the objective function
The objective function to minimize is: $1x_0 + 7x_1 + 3x_2 + 4x_3$

## Step 3: List all constraints
1. Storage space constraint for packs of napkins and paper towel rolls: $8x_1 + 7x_2 \geq 4$
2. Storage space constraint for cartons of milk and paper towel rolls: $5x_0 + 7x_2 \geq 8$
3. Total storage space constraint: $5x_0 + 8x_1 + 7x_2 + 2x_3 \geq 8$
4. Cost constraint for cartons of milk and paper towel rolls: $2x_0 + 6x_2 \geq 10$
5. Cost constraint for cartons of milk and cookies: $2x_0 + 7x_3 \geq 11$
6. Cost constraint for packs of napkins and paper towel rolls: $4x_1 + 6x_2 \geq 10$
7. Cost constraint for paper towel rolls and cookies: $6x_2 + 7x_3 \geq 13$
8. Cost constraint for cartons of milk, packs of napkins, and cookies: $2x_0 + 4x_1 + 7x_3 \geq 14$
9. Cost constraint for packs of napkins, paper towel rolls, and cookies: $4x_1 + 6x_2 + 7x_3 \geq 14$
10. Cost constraint for cartons of milk, packs of napkins, and cookies: $2x_0 + 4x_1 + 7x_3 \geq 13$
11. Cost constraint for all items: $2x_0 + 4x_1 + 6x_2 + 7x_3 \geq 13$
12. Constraint for cartons of milk and paper towel rolls: $4x_0 - 8x_2 \geq 0$
13. Constraint for cartons of milk and packs of napkins: $-8x_0 + 10x_1 \geq 0$
14. Storage space constraint for packs of napkins and cookies: $8x_1 + 2x_3 \leq 12$
15. Storage space constraint for cartons of milk and packs of napkins: $5x_0 + 8x_1 \leq 20$
16. Cost constraint for paper towel rolls and cookies: $6x_2 + 7x_3 \leq 53$
17. Cost constraint for cartons of milk and cookies: $2x_0 + 7x_3 \leq 72$
18. Cost constraint for cartons of milk and paper towel rolls: $2x_0 + 6x_2 \leq 46$
19. Cost constraint for packs of napkins and paper towel rolls: $4x_1 + 6x_2 \leq 46$
20. Cost constraint for cartons of milk, packs of napkins, and cookies: $2x_0 + 4x_1 + 7x_3 \leq 19$
21. Resource constraints:
- Storage space: $5x_0 + 8x_1 + 7x_2 + 2x_3 \leq 32$
- Dollar cost: $2x_0 + 4x_1 + 6x_2 + 7x_3 \leq 77$

## 4: Symbolic Representation
```json
{
'sym_variables': [('x0', 'cartons of milk'), ('x1', 'packs of napkins'), ('x2', 'paper towel rolls'), ('x3', 'cookies')],
'objective_function': '1*x0 + 7*x1 + 3*x2 + 4*x3',
'constraints': [
'8*x1 + 7*x2 >= 4',
'5*x0 + 7*x2 >= 8',
'5*x0 + 8*x1 + 7*x2 + 2*x3 >= 8',
'2*x0 + 6*x2 >= 10',
'2*x0 + 7*x3 >= 11',
'4*x1 + 6*x2 >= 10',
'6*x2 + 7*x3 >= 13',
'2*x0 + 4*x1 + 7*x3 >= 14',
'4*x1 + 6*x2 + 7*x3 >= 14',
'2*x0 + 4*x1 + 7*x3 >= 13',
'2*x0 + 4*x1 + 6*x2 + 7*x3 >= 13',
'4*x0 - 8*x2 >= 0',
'-8*x0 + 10*x1 >= 0',
'8*x1 + 2*x3 <= 12',
'5*x0 + 8*x1 <= 20',
'6*x2 + 7*x3 <= 53',
'2*x0 + 7*x3 <= 72',
'2*x0 + 6*x2 <= 46',
'4*x1 + 6*x2 <= 46',
'2*x0 + 4*x1 + 7*x3 <= 19',
'5*x0 + 8*x1 + 7*x2 + 2*x3 <= 32',
'2*x0 + 4*x1 + 6*x2 + 7*x3 <= 77'
]
}
```

## 5: Gurobi Code
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # cartons of milk
    x1 = model.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # packs of napkins
    x2 = model.addVar(name="x2", vtype=gurobi.GRB.INTEGER)  # paper towel rolls
    x3 = model.addVar(name="x3", vtype=gurobi.GRB.INTEGER)  # cookies

    # Objective function
    model.setObjective(1 * x0 + 7 * x1 + 3 * x2 + 4 * x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(8 * x1 + 7 * x2 >= 4)
    model.addConstr(5 * x0 + 7 * x2 >= 8)
    model.addConstr(5 * x0 + 8 * x1 + 7 * x2 + 2 * x3 >= 8)
    model.addConstr(2 * x0 + 6 * x2 >= 10)
    model.addConstr(2 * x0 + 7 * x3 >= 11)
    model.addConstr(4 * x1 + 6 * x2 >= 10)
    model.addConstr(6 * x2 + 7 * x3 >= 13)
    model.addConstr(2 * x0 + 4 * x1 + 7 * x3 >= 14)
    model.addConstr(4 * x1 + 6 * x2 + 7 * x3 >= 14)
    model.addConstr(2 * x0 + 4 * x1 + 7 * x3 >= 13)
    model.addConstr(2 * x0 + 4 * x1 + 6 * x2 + 7 * x3 >= 13)
    model.addConstr(4 * x0 - 8 * x2 >= 0)
    model.addConstr(-8 * x0 + 10 * x1 >= 0)
    model.addConstr(8 * x1 + 2 * x3 <= 12)
    model.addConstr(5 * x0 + 8 * x1 <= 20)
    model.addConstr(6 * x2 + 7 * x3 <= 53)
    model.addConstr(2 * x0 + 7 * x3 <= 72)
    model.addConstr(2 * x0 + 6 * x2 <= 46)
    model.addConstr(4 * x1 + 6 * x2 <= 46)
    model.addConstr(2 * x0 + 4 * x1 + 7 * x3 <= 19)
    model.addConstr(5 * x0 + 8 * x1 + 7 * x2 + 2 * x3 <= 32)
    model.addConstr(2 * x0 + 4 * x1 + 6 * x2 + 7 * x3 <= 77)

    # Solve the problem
    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Objective: {model.objval}")
        print(f"cartons of milk: {x0.varValue}")
        print(f"packs of napkins: {x1.varValue}")
        print(f"paper towel rolls: {x2.varValue}")
        print(f"cookies: {x3.varValue}")
    elif model.status == gurobi.GRB.INFEASIBLE:
        print("The problem is infeasible.")
    else:
        print("The problem has no optimal solution.")

optimize_problem()
```