## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'pickles', 'black beans', 'slices of pizza', and 'ham sandwiches', which we can denote as $x_1$, $x_2$, $x_3$, and $x_4$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $1 \times \text{pickles} + 8 \times \text{black beans} + 2 \times \text{slices of pizza} + 4 \times \text{ham sandwiches}$, which translates to $x_1 + 8x_2 + 2x_3 + 4x_4$.

## 3: Define the constraints in symbolic notation
The constraints given are:
1. $8x_1 + 6x_2 + x_3 + 7x_4 \leq 73$ (total calcium constraint)
2. $x_3 + 7x_4 \geq 14$ (calcium from pizza and ham sandwiches)
3. $6x_2 + 7x_4 \geq 7$ (calcium from black beans and ham sandwiches)
4. $8x_1 + x_3 \geq 8$ (calcium from pickles and pizza)
5. $x_3 + 7x_4 \leq 33$ (calcium from pizza and ham sandwiches, upper bound)
6. $6x_2 + x_3 \leq 64$ (calcium from black beans and pizza)
7. $6x_2 + 7x_4 \leq 58$ (calcium from black beans and ham sandwiches)
8. $8x_1 + x_3 \leq 33$ (calcium from pickles and pizza, upper bound)
9. $8x_1 + 7x_4 \leq 30$ (calcium from pickles and ham sandwiches)
10. $8x_1 + 6x_2 + x_3 \leq 69$ (calcium from pickles, black beans, and pizza)
11. $6x_2 + x_3 + 7x_4 \leq 28$ (calcium from black beans, pizza, and ham sandwiches)
12. $8x_1 + 6x_2 + x_3 + 7x_4 \leq 28$ (total calcium, specific upper bound)

## 4: Specify the symbolic variables and constraints for output
The symbolic variables are:
- $x_1$ for 'pickles'
- $x_2$ for 'black beans'
- $x_3$ for 'slices of pizza'
- $x_4$ for 'ham sandwiches'

## 5: Output the symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'pickles'), ('x2', 'black beans'), ('x3', 'slices of pizza'), ('x4', 'ham sandwiches')],
    'objective_function': 'x1 + 8x2 + 2x3 + 4x4',
    'constraints': [
        '8x1 + 6x2 + x3 + 7x4 <= 73',
        'x3 + 7x4 >= 14',
        '6x2 + 7x4 >= 7',
        '8x1 + x3 >= 8',
        'x3 + 7x4 <= 33',
        '6x2 + x3 <= 64',
        '6x2 + 7x4 <= 58',
        '8x1 + x3 <= 33',
        '8x1 + 7x4 <= 30',
        '8x1 + 6x2 + x3 <= 69',
        '6x2 + x3 + 7x4 <= 28',
        '8x1 + 6x2 + x3 + 7x4 <= 28'
    ]
}
```

## 6: Implement the problem in Gurobi
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x1 = m.addVar(name='pickles', vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name='black_beans', vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name='slices_of_pizza', vtype=gurobi.GRB.INTEGER)
x4 = m.addVar(name='ham_sandwiches')

# Objective function
m.setObjective(x1 + 8*x2 + 2*x3 + 4*x4, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(8*x1 + 6*x2 + x3 + 7*x4 <= 73)
m.addConstr(x3 + 7*x4 >= 14)
m.addConstr(6*x2 + 7*x4 >= 7)
m.addConstr(8*x1 + x3 >= 8)
m.addConstr(x3 + 7*x4 <= 33)
m.addConstr(6*x2 + x3 <= 64)
m.addConstr(6*x2 + 7*x4 <= 58)
m.addConstr(8*x1 + x3 <= 33)
m.addConstr(8*x1 + 7*x4 <= 30)
m.addConstr(8*x1 + 6*x2 + x3 <= 69)
m.addConstr(6*x2 + x3 + 7*x4 <= 28)
m.addConstr(8*x1 + 6*x2 + x3 + 7*x4 <= 28)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('Pickles: ', x1.varValue)
    print('Black beans: ', x2.varValue)
    print('Slices of pizza: ', x3.varValue)
    print('Ham sandwiches: ', x4.varValue)
else:
    print('The model is infeasible')
```