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

- $x_1$ as the number of pairs of earrings produced,
- $x_2$ as the number of watches produced.

The objective function is to maximize profit. Given that the profit from selling a pair of earrings is $45 and from selling a watch is $70, the objective function can be represented algebraically as:

\[ 45x_1 + 70x_2 \]

The constraints are based on the availability of machines and the time required for each product:

1. The heating machine is available for at most 14 hours. It takes 2 hours to make a pair of earrings and 3.5 hours to make a watch, so we have:
\[ 2x_1 + 3.5x_2 \leq 14 \]

2. The polishing machine is available for at most 10 hours. It takes 1.5 hours to make a pair of earrings and 2 hours to make a watch, so we have:
\[ 1.5x_1 + 2x_2 \leq 10 \]

Additionally, $x_1$ and $x_2$ must be non-negative since they represent quantities of products.

In symbolic representation with natural language objects:

```json
{
    'sym_variables': [('x1', 'number of pairs of earrings'), ('x2', 'number of watches')],
    'objective_function': '45*x1 + 70*x2',
    'constraints': ['2*x1 + 3.5*x2 <= 14', '1.5*x1 + 2*x2 <= 10', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's write the Gurobi code to solve this problem:

```python
from gurobipy import *

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

# Add variables
x1 = m.addVar(lb=0, name="pairs_of_earrings")
x2 = m.addVar(lb=0, name="watches")

# Set the objective function
m.setObjective(45*x1 + 70*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(2*x1 + 3.5*x2 <= 14, "heating_machine")
m.addConstr(1.5*x1 + 2*x2 <= 10, "polishing_machine")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: x1 = {x1.x}, x2 = {x2.x}")
    print(f"Maximum profit: {m.objVal}")
else:
    print("No optimal solution found")
```