## Problem Description and Symbolic Representation

The problem requires maximizing the objective function \(7 \times \text{milkshakes} + 1 \times \text{sashimi}\) subject to several constraints.

### Symbolic Variables:
- \(x_1\) represents 'milkshakes'
- \(x_2\) represents 'sashimi'

### Objective Function:
The objective function to maximize is \(7x_1 \times x_2\).

### Constraints:
1. \(2x_1 + 12x_2 \geq 31\) (At least 31 milligrams of calcium must come from milkshakes and sashimi)
2. \(-6x_1 + 7x_2 \geq 0\) (\(-6\) times the number of milkshakes, plus 7 times the number of sashimi must be at least zero)
3. \(2x_1 + 12x_2 \leq 52\) (No more than 52 milligrams of calcium from milkshakes and sashimi)
4. \(2x_1 + 12x_2 \leq 52\) (Duplicate constraint, ensuring no more than 52 milligrams of calcium)
5. \(x_1 \in \mathbb{Z}\) (There must be a nonfractional number of milkshakes)
6. \(x_2 \in \mathbb{Z}\) (You have to have a whole number of sashimi)

## Symbolic Representation in JSON Format

```json
{
  'sym_variables': [('x1', 'milkshakes'), ('x2', 'sashimi')],
  'objective_function': '7*x1*x2',
  'constraints': [
    '2*x1 + 12*x2 >= 31',
    '-6*x1 + 7*x2 >= 0',
    '2*x1 + 12*x2 <= 52',
    '2*x1 + 12*x2 <= 52',
    'x1 ∈ ℤ',
    'x2 ∈ ℤ'
  ]
}
```

## Gurobi Code

```python
import gurobi

def solve_optimization_problem():
    # Create a new Gurobi model
    model = gurobi.Model()

    # Define variables
    milkshakes = model.addVar(name='milkshakes', vtype=gurobi.GRB.INTEGER)
    sashimi = model.addVar(name='sashimi', vtype=gurobi.GRB.INTEGER)

    # Objective function: maximize 7 * milkshakes * sashimi
    # Since Gurobi does not directly support nonlinear objective functions in the standard API,
    # we will have to manipulate this. However, for simplicity and adherence to common practices,
    # let's approximate or directly tackle it with suitable methods.

    # However, the objective function 7 * milkshakes * sashimi is a product of two variables,
    # which makes it a nonlinear problem. Gurobi can handle this but requires a different approach.

    # For simplicity, let's reformulate it as a MILP if possible or use a suitable method.

    # Here, let's assume we are maximizing 7*milkshakes*sashimi directly might not be straightforward
    # We can use a piecewise or a big-M method for such problems but let's assume a direct formulation.

    model.setObjective(7 * milkshakes * sashimi, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(2 * milkshakes + 12 * sashimi >= 31)
    model.addConstr(-6 * milkshakes + 7 * sashimi >= 0)
    model.addConstr(2 * milkshakes + 12 * sashimi <= 52)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Milkshakes: {milkshakes.varValue}")
        print(f"Sashimi: {sashimi.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("The model is infeasible or unbounded.")

solve_optimization_problem()
```