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

- $x_1$ as the number of large salads made
- $x_2$ as the number of small salads made

The objective function aims to maximize profit. Given that the profit per large salad is $4 and the profit per small salad is $2, the objective function can be represented algebraically as:

$$\text{Maximize: } 4x_1 + 2x_2$$

The constraints are based on the availability of lettuce and sauce. A large salad takes 45g of lettuce and 10g of sauce, while a small salad takes 30g of lettuce and 7g of sauce. The shop has available 1500g of lettuce and 1200g of sauce. Thus, the constraints can be represented as:

- For lettuce: $45x_1 + 30x_2 \leq 1500$
- For sauce: $10x_1 + 7x_2 \leq 1200$

Additionally, since we cannot make a negative number of salads, we have non-negativity constraints:

- $x_1 \geq 0$
- $x_2 \geq 0$

The symbolic representation in the requested format is:
```json
{
    'sym_variables': [('x1', 'number of large salads'), ('x2', 'number of small salads')],
    'objective_function': '4*x1 + 2*x2',
    'constraints': ['45*x1 + 30*x2 <= 1500', '10*x1 + 7*x2 <= 1200', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this problem using Gurobi in Python:
```python
from gurobipy import *

# Create a new model
m = Model("Salad_Shop_Optimization")

# Define variables
x1 = m.addVar(lb=0, name="large_salads")
x2 = m.addVar(lb=0, name="small_salads")

# Set the objective function
m.setObjective(4*x1 + 2*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(45*x1 + 30*x2 <= 1500, "lettuce_constraint")
m.addConstr(10*x1 + 7*x2 <= 1200, "sauce_constraint")

# Optimize model
m.optimize()

# Print results
for v in m.getVars():
    print(f"{v.varName}: {v.x}")

print("Objective:", m.objVal)
```