To solve the given optimization problem, we first need to define the variables and the objective function symbolically. Let's denote:

- $x_1$ as the number of new grad engineers,
- $x_2$ as the number of senior engineers.

The objective is to minimize the total wage bill, which can be represented as $1000x_1 + 3000x_2$.

The constraints given are:
1. The total weekly wage bill must be kept below $100,000: $1000x_1 + 3000x_2 \leq 100,000$.
2. The projects require a minimum of 50 engineers: $x_1 + x_2 \geq 50$.
3. At least 10 engineers must be senior engineers: $x_2 \geq 10$.
4. The number of senior engineers should be at least a third the number of new grad engineers: $x_2 \geq \frac{1}{3}x_1$.

Symbolically, our problem can be represented as:
```json
{
    'sym_variables': [('x1', 'number of new grad engineers'), ('x2', 'number of senior engineers')],
    'objective_function': '1000*x1 + 3000*x2',
    'constraints': [
        '1000*x1 + 3000*x2 <= 100000',
        'x1 + x2 >= 50',
        'x2 >= 10',
        'x2 >= (1/3)*x1'
    ]
}
```

Now, let's implement this problem in Gurobi using Python:
```python
from gurobipy import *

# Create a new model
model = Model("Engineering_Company_Optimization")

# Define the variables
x1 = model.addVar(vtype=GRB.INTEGER, name="new_grad_engineers")
x2 = model.addVar(vtype=GRB.INTEGER, name="senior_engineers")

# Set the objective function
model.setObjective(1000*x1 + 3000*x2, GRB.MINIMIZE)

# Add constraints
model.addConstr(1000*x1 + 3000*x2 <= 100000, "wage_bill_constraint")
model.addConstr(x1 + x2 >= 50, "total_engineers_constraint")
model.addConstr(x2 >= 10, "senior_engineers_minimum_constraint")
model.addConstr(x2 >= (1/3)*x1, "senior_to_new_grad_ratio_constraint")

# Optimize the model
model.optimize()

# Print the results
if model.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of new grad engineers: {x1.x}")
    print(f"Number of senior engineers: {x2.x}")
    print(f"Total wage bill: ${1000*x1.x + 3000*x2.x}")
else:
    print("No optimal solution found")
```