To solve this problem, we first need to define the decision variables and the objective function. Let's denote the number of platinum necklaces as \(P\) and the number of silver necklaces as \(S\). The objective is to maximize profit, which is $2000 per platinum necklace and $700 per silver necklace. Thus, our objective function can be written as:

\[ \text{Maximize:} \quad 2000P + 700S \]

We have two main constraints based on the availability of the designing and crafting teams:

1. Designing team constraint: 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 us the constraint:

\[ 4P + 7S \leq 35 \]

2. Crafting team constraint: 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 us the constraint:

\[ 15P + 5S \leq 40 \]

Additionally, \(P\) and \(S\) must be non-negative since we cannot produce a negative number of necklaces.

Now, let's translate this into Gurobi code in Python:

```python
from gurobipy import *

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

# Define the decision variables
P = m.addVar(vtype=GRB.INTEGER, name="Platinum_Necklaces")
S = m.addVar(vtype=GRB.INTEGER, name="Silver_Necklaces")

# Set the objective function
m.setObjective(2000*P + 700*S, GRB.MAXIMIZE)

# Add constraints
m.addConstr(4*P + 7*S <= 35, "Designing_Team_Constraint")
m.addConstr(15*P + 5*S <= 40, "Crafting_Team_Constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Platinum Necklaces: {P.x}")
    print(f"Silver Necklaces: {S.x}")
    print(f"Maximum Profit: ${2000*P.x + 700*S.x}")
else:
    print("No optimal solution found")
```