## Symbolic Representation

The problem can be converted into a symbolic representation as follows:

Let's denote:
- $x_1$ as the number of ring layouts
- $x_2$ as the number of tree layouts
- $x_3$ as the number of mesh layouts

The objective function to maximize profit is:
\[ \text{Maximize:} \quad 2000x_1 + 4000x_2 + 8000x_3 \]

The constraints based on the available resources are:
\[ 50x_1 + 30x_2 + 100x_3 \leq 2000 \] (workstations)
\[ 20x_1 + 15x_2 + 50x_3 \leq 500 \] (servers)
\[ 10x_1 + 7x_2 + 30x_3 \leq 300 \] (switches)
\[ x_1, x_2, x_3 \geq 0 \] (non-negativity)

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'ring layouts'), ('x2', 'tree layouts'), ('x3', 'mesh layouts')],
    'objective_function': '2000*x1 + 4000*x2 + 8000*x3',
    'constraints': [
        '50*x1 + 30*x2 + 100*x3 <= 2000',
        '20*x1 + 15*x2 + 50*x3 <= 500',
        '10*x1 + 7*x2 + 30*x3 <= 300',
        'x1 >= 0',
        'x2 >= 0',
        'x3 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Network_Optimization")

# Define variables
x1 = model.addVar(name="ring_layouts", lb=0, vtype=gp.GRB.INTEGER)  # Number of ring layouts
x2 = model.addVar(name="tree_layouts", lb=0, vtype=gp.GRB.INTEGER)  # Number of tree layouts
x3 = model.addVar(name="mesh_layouts", lb=0, vtype=gp.GRB.INTEGER)  # Number of mesh layouts

# Objective function: Maximize profit
model.setObjective(2000*x1 + 4000*x2 + 8000*x3, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(50*x1 + 30*x2 + 100*x3 <= 2000, name="workstations")  # Workstations constraint
model.addConstr(20*x1 + 15*x2 + 50*x3 <= 500, name="servers")  # Servers constraint
model.addConstr(10*x1 + 7*x2 + 30*x3 <= 300, name="switches")  # Switches constraint

# Solve the model
model.optimize()

# Print solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Ring Layouts: {x1.varValue}")
    print(f"Tree Layouts: {x2.varValue}")
    print(f"Mesh Layouts: {x3.varValue}")
    print(f"Maximum Profit: {model.objVal}")
else:
    print("No optimal solution found.")
```