## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'steaks' and 'sashimi', which can be represented symbolically as $x_1$ and $x_2$ respectively. The objective function to minimize is $4.37x_1 + 5.64x_2$. The constraints are:
- $5x_1 + 6x_2 \geq 35$ (at least 35 milligrams of iron from steaks and sashimi)
- $5x_1 \geq 35$ and $6x_2 \geq 35$ are not correct representations; instead, we have: $5x_1 + 6x_2 \geq 35$ and also $x_1, x_2 \geq 0$ implicitly
- $4x_1 + 10x_2 \geq 45$ (at least 45 milligrams of calcium from steaks and sashimi)
- $-3x_1 + 6x_2 \geq 0$
- $5x_1 + 6x_2 \leq 165$ (at most 165 milligrams of iron from steaks and sashimi)
- $4x_1 + 10x_2 \leq 97$ (at most 97 milligrams of calcium from steaks and sashimi)
- $x_1$ is a continuous variable (number of steaks does not have to be an integer)
- $x_2$ is an integer variable (limited to a whole number of sashimi)

## 2: Correct and list all constraints properly
Correcting and listing all constraints:
1. $5x_1 + 6x_2 \geq 35$
2. $4x_1 + 10x_2 \geq 45$
3. $-3x_1 + 6x_2 \geq 0$
4. $5x_1 + 6x_2 \leq 165$
5. $4x_1 + 10x_2 \leq 97$

## 3: Symbolic Representation
The symbolic representation of the problem is:
```json
{
'sym_variables': [('x1', 'steaks'), ('x2', 'sashimi')],
'objective_function': '4.37*x1 + 5.64*x2',
'constraints': [
    '5*x1 + 6*x2 >= 35',
    '4*x1 + 10*x2 >= 45',
    '-3*x1 + 6*x2 >= 0',
    '5*x1 + 6*x2 <= 165',
    '4*x1 + 10*x2 <= 97'
]
}
```

## 4: Gurobi Code
Now, let's implement this problem using Gurobi in Python:
```python
import gurobi

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

    # Define variables
    steaks = model.addVar(name="steaks", lb=0, ub=float('inf'))  # Continuous variable
    sashimi = model.addVar(name="sashimi", lb=0, vtype=gurobi.GRB.INTEGER)  # Integer variable

    # Objective function
    model.setObjective(4.37 * steaks + 5.64 * sashimi, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(5 * steaks + 6 * sashimi >= 35, name="iron_requirement")
    model.addConstr(4 * steaks + 10 * sashimi >= 45, name="calcium_requirement")
    model.addConstr(-3 * steaks + 6 * sashimi >= 0, name="sashimi_vs_steak")
    model.addConstr(5 * steaks + 6 * sashimi <= 165, name="max_iron")
    model.addConstr(4 * steaks + 10 * sashimi <= 97, name="max_calcium")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: steaks = {steaks.varValue}, sashimi = {sashimi.varValue}")
    else:
        print("No optimal solution found")

solve_optimization_problem()
```