To solve this optimization problem, we need to first convert the natural language description into a symbolic representation. 

Let's define the variables as follows:
- $x_1$ represents the number of Caesar salads made.
- $x_2$ represents the number of Mediterranean salads made.

The objective function is to maximize profit. The profit per Caesar salad is $7, and the profit per Mediterranean salad is $9. Therefore, the objective function can be represented algebraically as:
\[ 7x_1 + 9x_2 \]

The constraints are based on the availability of lettuce, sauce, and cheese:
- Lettuce: Each Caesar salad uses 100 g of lettuce, and each Mediterranean salad uses 150 g. The total available is 20000 g. This constraint can be represented as:
\[ 100x_1 + 150x_2 \leq 20000 \]
- Sauce: Each Caesar salad uses 10 g of sauce, and each Mediterranean salad uses 15 g. The total available is 2000 g. This constraint can be represented as:
\[ 10x_1 + 15x_2 \leq 2000 \]
- Cheese: Each Caesar salad uses 5 g of cheese, and each Mediterranean salad uses 15 g. The total available is 3000 g. This constraint can be represented as:
\[ 5x_1 + 15x_2 \leq 3000 \]

Additionally, we have non-negativity constraints since the number of salads cannot be negative:
\[ x_1 \geq 0, x_2 \geq 0 \]

Therefore, in symbolic representation, our problem is:
```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']
}
```

To solve this problem using Gurobi in Python, we can use the following code:
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="Caesar_Salad", lb=0)
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="Mediterranean_Salad", lb=0)

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

# Add constraints
m.addConstr(100*x1 + 150*x2 <= 20000, "Lettuce_Constraint")
m.addConstr(10*x1 + 15*x2 <= 2000, "Sauce_Constraint")
m.addConstr(5*x1 + 15*x2 <= 3000, "Cheese_Constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Caesar Salads: {x1.x}")
    print(f"Mediterranean Salads: {x2.x}")
    print(f"Maximum Profit: {m.objVal}")
else:
    print("No optimal solution found.")
```