## Symbolic Representation

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

* Variables: 
  - 'x1', 'sapphire rings'
  - 'x2', 'ruby rings'

* Objective Function: Maximize 500*x1 + 400*x2

* Constraints:
  - x1 ≤ 10 (sapphire team production limit)
  - x2 ≤ 15 (ruby team production limit)
  - x1 + x2 ≤ 15 (master jeweler approval limit)
  - x1, x2 ≥ 0 (non-negativity constraint, as the number of rings cannot be negative)

In JSON format, this is:

```json
{
    'sym_variables': [('x1', 'sapphire rings'), ('x2', 'ruby rings')],
    'objective_function': '500*x1 + 400*x2',
    'constraints': ['x1 <= 10', 'x2 <= 15', 'x1 + x2 <= 15', 'x1 >= 0', 'x2 >= 0']
}
```

## Gurobi Code

Here is the Gurobi code in Python to solve this problem:

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="sapphire_rings", lb=0, ub=10, vtype=gp.GRB.INTEGER)
x2 = model.addVar(name="ruby_rings", lb=0, ub=15, vtype=gp.GRB.INTEGER)

# Set objective function
model.setObjective(500*x1 + 400*x2, gp.GRB.MAXIMIZE)

# Add constraints
model.addConstr(x1 <= 10, name="sapphire_team_limit")
model.addConstr(x2 <= 15, name="ruby_team_limit")
model.addConstr(x1 + x2 <= 15, name="master_jeweler_limit")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Sapphire rings: {x1.varValue}")
    print(f"Ruby rings: {x2.varValue}")
    print(f"Max Profit: {model.objVal}")
else:
    print("No optimal solution found.")
```