## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the number of platinum necklaces
- $x_2$ represents the number of silver necklaces

## Step 2: Translate the objective function into symbolic notation
The profit is $2000 per platinum necklace and $700 per silver necklace. The objective function to maximize profit ($P$) is:
\[ P = 2000x_1 + 700x_2 \]

## 3: Translate the constraints into symbolic notation
- Each platinum necklace takes 4 hours to design, and each silver necklace takes 7 hours to design. The designing team is available for 35 hours. This gives the constraint:
\[ 4x_1 + 7x_2 \leq 35 \]
- Each platinum necklace takes 15 hours to craft, and each silver necklace takes 5 hours to craft. The crafting team is available for 40 hours. This gives the constraint:
\[ 15x_1 + 5x_2 \leq 40 \]
- Additionally, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of necklaces cannot be negative.

## 4: Express the problem in the required JSON format
```json
{
    'sym_variables': [('x1', 'platinum necklaces'), ('x2', 'silver necklaces')],
    'objective_function': '2000*x1 + 700*x2',
    'constraints': [
        '4*x1 + 7*x2 <= 35',
        '15*x1 + 5*x2 <= 40',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 5: Implement the problem in Gurobi code
```python
import gurobi

def solve_necklace_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name='platinum_necklaces', lb=0, vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='silver_necklaces', lb=0, vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(2000 * x1 + 700 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(4 * x1 + 7 * x2 <= 35, name='designing_time')
    model.addConstr(15 * x1 + 5 * x2 <= 40, name='crafting_time')

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
        print(f"Maximum profit: ${2000 * x1.x + 700 * x2.x}")
    else:
        print("The model is infeasible")

solve_necklace_problem()
```