## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'black beans' and 'steaks', which we can denote as $x_1$ and $x_2$ respectively. The objective function to minimize is $1x_1 + 7x_2$. The constraints are:
- $x_1 + 9x_2 \geq 18$ (at least 18 milligrams of iron),
- $3x_1 + 7x_2 \geq 22$ (at least $22 on black beans and steaks),
- $x_1 + 3x_2 \geq 11$ (at least 11 grams of fiber),
- $10x_1 - x_2 \geq 0$ (specific relationship between black beans and steaks),
- $x_1 + 9x_2 \leq 71$ (at most 71 milligrams of iron),
- $3x_1 + 7x_2 \leq 45$ (at most $45 on black beans and steaks),
- $x_1 + 3x_2 \leq 28$ (at most 28 grams of fiber).

## Step 2: Identify the symbolic variables and constraints
The symbolic variables are:
- $x_1$ for 'black beans',
- $x_2$ for 'steaks'.

The objective function is: $1x_1 + 7x_2$.

The constraints in symbolic form are:
- $x_1 + 9x_2 \geq 18$,
- $3x_1 + 7x_2 \geq 22$,
- $x_1 + 3x_2 \geq 11$,
- $10x_1 - x_2 \geq 0$,
- $x_1 + 9x_2 \leq 71$,
- $3x_1 + 7x_2 \leq 45$,
- $x_1 + 3x_2 \leq 28$.

## 3: Consider the integer constraint
$x_2$ must be an integer (since there cannot be a non-integer number of steaks), but $x_1$ can be fractional.

## 4: Formulate the problem in Gurobi
To formulate this problem in Gurobi, we need to:
- Define the variables with their respective properties (e.g., integer or continuous),
- Define the objective function,
- Define the constraints.

## 5: Write the Gurobi code
```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="black_beans", lb=0)  # Continuous variable for black beans
    x2 = model.addVar(name="steaks", lb=0, integrality=gurobi.GRB.INTEGER)  # Integer variable for steaks

    # Define objective function
    model.setObjective(x1 + 7 * x2, gurobi.GRB.MINIMIZE)

    # Define constraints
    model.addConstr(x1 + 9 * x2 >= 18, name="iron_constraint")
    model.addConstr(3 * x1 + 7 * x2 >= 22, name="cost_constraint")
    model.addConstr(x1 + 3 * x2 >= 11, name="fiber_constraint")
    model.addConstr(10 * x1 - x2 >= 0, name="relationship_constraint")
    model.addConstr(x1 + 9 * x2 <= 71, name="max_iron_constraint")
    model.addConstr(3 * x1 + 7 * x2 <= 45, name="max_cost_constraint")
    model.addConstr(x1 + 3 * x2 <= 28, name="max_fiber_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Black beans: {x1.varValue}")
        print(f"Steaks: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```

## 6: Symbolic Representation
The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'black beans'), ('x2', 'steaks')],
    'objective_function': '1*x1 + 7*x2',
    'constraints': [
        'x1 + 9*x2 >= 18',
        '3*x1 + 7*x2 >= 22',
        'x1 + 3*x2 >= 11',
        '10*x1 - x2 >= 0',
        'x1 + 9*x2 <= 71',
        '3*x1 + 7*x2 <= 45',
        'x1 + 3*x2 <= 28'
    ]
}
```