## Problem Description and Formulation

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

### Variables and Parameters

- **Variables:**
  - \(\text{milkshakes}\): The number of milkshakes.
  - \(\text{sashimi}\): The number of sashimi.

- **Attributes/ Resources:**
  - \(r0\): Milligrams of calcium.
    - \(\text{milkshakes}\) contain 2 milligrams of calcium.
    - \(\text{sashimi}\) contain 12 milligrams of calcium.
    - Upper bound for calcium intake: 102 milligrams.
    - Initial conditions or specific values: Not directly relevant but bounds are.

### Constraints

1. **Calcium from Milkshakes and Sashimi**: 
   - At least 31 milligrams of calcium must come from \(\text{milkshakes}\) and \(\text{sashimi}\): \(2 \times \text{milkshakes} + 12 \times \text{sashimi} \geq 31\).
   - No more than 52 milligrams of calcium from \(\text{milkshakes}\) and \(\text{sashimi}\): \(2 \times \text{milkshakes} + 12 \times \text{sashimi} \leq 52\).

2. **Linear Constraint**:
   - \(-6 \times \text{milkshakes} + 7 \times \text{sashimi} \geq 0\).

3. **Integrality Constraints**:
   - \(\text{milkshakes}\) must be a non-fractional (integer) number.
   - \(\text{sashimi}\) must be a whole (integer) number.

### Objective Function

Maximize: \(7 \times (\text{milkshakes} + 1) \times \text{sashimi}\).

## Gurobi Code Formulation

```python
import gurobi

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

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

    # Objective function
    model.setObjective(7 * (milkshakes + 1) * sashimi, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(2 * milkshakes + 12 * sashimi >= 31, name="calcium_min")
    model.addConstr(2 * milkshakes + 12 * sashimi <= 52, name="calcium_max")
    model.addConstr(-6 * milkshakes + 7 * sashimi >= 0, name="linear_constraint")

    # Calcium bounds from the problem description
    # Not necessary to explicitly define r0 as it's already considered in constraints

    # 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")

solve_optimization_problem()
```

This code defines the optimization problem as per the given description and attempts to solve it using Gurobi. If a feasible solution exists, it prints out the optimal values for \(\text{milkshakes}\) and \(\text{sashimi}\) along with the maximum objective function value. If the problem is infeasible, it indicates so.