## Symbolic Representation

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

Let's define the symbolic variables as follows:
- $x_1$ represents the number of round watches made by team A.
- $x_2$ represents the number of square watches made by team B.

The objective is to maximize profit. Given that the profit per round watch is $1000 and the profit per square watch is $1250, the objective function can be represented as:

Maximize: $1000x_1 + 1250x_2$

The constraints based on the problem description are:
- Team A can make at most 5 round watches a day: $x_1 \leq 5$
- Team B can make at most 6 square watches a day: $x_2 \leq 6$
- The senior watchmaker can check at most 8 watches total a day: $x_1 + x_2 \leq 8$
- Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$ (since the number of watches cannot be negative)

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'round watches'), ('x2', 'square watches')],
    'objective_function': '1000*x1 + 1250*x2',
    'constraints': [
        'x1 <= 5',
        'x2 <= 6',
        'x1 + x2 <= 8',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define the variables
x1 = model.addVar(name="round_watches", lb=0, ub=5, vtype=gp.GRB.INTEGER)  # Round watches
x2 = model.addVar(name="square_watches", lb=0, ub=6, vtype=gp.GRB.INTEGER)  # Square watches

# Objective function: Maximize profit
model.setObjective(1000*x1 + 1250*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(x1 <= 5, name="Team_A_capacity")
model.addConstr(x2 <= 6, name="Team_B_capacity")
model.addConstr(x1 + x2 <= 8, name="Watchmaker_capacity")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: Round watches = {x1.varValue}, Square watches = {x2.varValue}")
    print(f"Max Profit: ${1000*x1.varValue + 1250*x2.varValue}")
else:
    print("No optimal solution found")
```