## Step 1: Define the symbolic representation of the problem

Let's denote the number of Caesar salads as $x_1$ and the number of Mediterranean salads as $x_2$. The objective is to maximize profit, which is $7x_1 + 9x_2$. The constraints are based on the available amounts of lettuce, sauce, and cheese.

## Step 2: Formulate the objective function and constraints in symbolic notation

- **Variables:** $(x_1, \text{Caesar salad})$, $(x_2, \text{Mediterranean salad})$
- **Objective Function:** $7x_1 + 9x_2$
- **Constraints:**
  1. Lettuce: $100x_1 + 150x_2 \leq 20000$
  2. Sauce: $10x_1 + 15x_2 \leq 2000$
  3. Cheese: $5x_1 + 15x_2 \leq 3000$
  4. Non-negativity: $x_1 \geq 0$, $x_2 \geq 0$

## 3: Convert the problem into a JSON object for clarity

```json
{
  'sym_variables': [('x1', 'Caesar salad'), ('x2', 'Mediterranean salad')],
  'objective_function': '7*x1 + 9*x2',
  'constraints': [
    '100*x1 + 150*x2 <= 20000',
    '10*x1 + 15*x2 <= 2000',
    '5*x1 + 15*x2 <= 3000',
    '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="Caesar_salad", lb=0, ub=gurobi.GRB.INFINITY)
    x2 = model.addVar(name="Mediterranean_salad", lb=0, ub=gurobi.GRB.INFINITY)

    # Set objective function
    model.setObjective(7*x1 + 9*x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(100*x1 + 150*x2 <= 20000, name="Lettuce_constraint")
    model.addConstr(10*x1 + 15*x2 <= 2000, name="Sauce_constraint")
    model.addConstr(5*x1 + 15*x2 <= 3000, name="Cheese_constraint")

    # Optimize model
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Caesar salads: {x1.varValue}")
        print(f"Mediterranean salads: {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_salad_problem()
```