To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's define:

- $x_1$ as the number of individual salads sold.
- $x_2$ as the number of family-sized salads sold.

The objective function, which represents the total profit, can be written as:
\[ 4x_1 + 7x_2 \]

This is because each individual salad gives a profit of $4 and each family-sized salad gives a profit of $7.

Now, let's consider the constraints based on the available ingredients:

1. Lettuce constraint: The store has 220 units of lettuce. Each individual salad uses 5 units, and each family-sized salad uses 18 units. So, the total use of lettuce must not exceed 220 units:
\[ 5x_1 + 18x_2 \leq 220 \]

2. Tomatoes constraint: The store has 150 units of tomatoes. Each individual salad uses 2 units, and each family-sized salad uses 6 units. So, the total use of tomatoes must not exceed 150 units:
\[ 2x_1 + 6x_2 \leq 150 \]

3. Sauce constraint: The store has 140 units of sauce. Each individual salad uses 2 units, and each family-sized salad uses 5 units. So, the total use of sauce must not exceed 140 units:
\[ 2x_1 + 5x_2 \leq 140 \]

4. Non-negativity constraints: Since we cannot sell a negative number of salads, both $x_1$ and $x_2$ must be non-negative:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

Now, let's represent this problem in the requested format:

```json
{
    'sym_variables': [('x1', 'number of individual salads'), ('x2', 'number of family-sized salads')],
    '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'
    ]
}
```

And here is the Gurobi code to solve this problem:

```python
from gurobipy import *

# Create a new model
model = Model("Salad_Sales")

# Define variables
x1 = model.addVar(vtype=GRB.CONTINUOUS, name="individual_salads")
x2 = model.addVar(vtype=GRB.CONTINUOUS, name="family_sized_salads")

# Set the objective function
model.setObjective(4*x1 + 7*x2, GRB.MAXIMIZE)

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

# Optimize the model
model.optimize()

# Print the results
if model.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Individual salads: {x1.x}")
    print(f"Family-sized salads: {x2.x}")
    print(f"Total profit: ${4*x1.x + 7*x2.x:.2f}")
else:
    print("No optimal solution found.")
```