## Step 1: Define the symbolic representation of the problem
Let's denote the number of individual salads as $x_1$ and the number of family-sized salads as $x_2$. The objective is to maximize profit, which is $4x_1 + 7x_2$. The constraints based on the available ingredients are:
- Lettuce: $5x_1 + 18x_2 \leq 220$
- Tomatoes: $2x_1 + 6x_2 \leq 150$
- Sauce: $2x_1 + 5x_2 \leq 140$
Also, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of salads cannot be negative.

## 2: Convert the problem into a Gurobi-compatible format
The symbolic representation is:
- Variables: $x_1$ (individual salad), $x_2$ (family-sized salad)
- Objective function: $4x_1 + 7x_2$
- Constraints:
  1. $5x_1 + 18x_2 \leq 220$
  2. $2x_1 + 6x_2 \leq 150$
  3. $2x_1 + 5x_2 \leq 140$
  4. $x_1 \geq 0$
  5. $x_2 \geq 0$

## 3: Express the problem in JSON format as requested
```json
{
'sym_variables': [('x1', 'individual salad'), ('x2', 'family-sized salad')],
'objective_function': '4*x1 + 7*x2',
'constraints': [
    '5*x1 + 18*x2 <= 220',
    '2*x1 + 6*x2 <= 150',
    '2*x1 + 5*x2 <= 140',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 4: Implement the problem in Gurobi Python
```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="individual_salad", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name="family_sized_salad", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Objective function: maximize 4*x1 + 7*x2
    model.setObjective(4*x1 + 7*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(5*x1 + 18*x2 <= 220, name="lettuce_constraint")
    model.addConstr(2*x1 + 6*x2 <= 150, name="tomatoes_constraint")
    model.addConstr(2*x1 + 5*x2 <= 140, name="sauce_constraint")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Individual salads: {x1.varValue}")
        print(f"Family-sized salads: {x2.varValue}")
        print(f"Max profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_salad_problem()
```