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

- $x_1$ as the number of one-inch binders made.
- $x_2$ as the number of two-inch binders made.

The objective function is to maximize profit. Given that the profit per one-inch binder is $1 and the profit per two-inch binder is $2, the objective function can be represented algebraically as:

\[ \text{Maximize:} \quad 1x_1 + 2x_2 \]

The constraints based on the problem description are:

1. The company must make at least 60 one-inch binders: $x_1 \geq 60$
2. The company must make at least 70 two-inch binders: $x_2 \geq 70$
3. The company can make at most 150 one-inch binders: $x_1 \leq 150$
4. The company can make at most 160 two-inch binders: $x_2 \leq 160$
5. The company has a contract to send at least 200 binders of either type: $x_1 + x_2 \geq 200$

Thus, the symbolic representation of the problem is:

```json
{
    'sym_variables': [('x1', 'number of one-inch binders'), ('x2', 'number of two-inch binders')],
    'objective_function': 'Maximize: 1*x1 + 2*x2',
    'constraints': ['x1 >= 60', 'x2 >= 70', 'x1 <= 150', 'x2 <= 160', 'x1 + x2 >= 200']
}
```

To solve this problem using Gurobi in Python, we can use the following code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=60, ub=150, vtype=GRB.INTEGER, name="one_inch_binders")
x2 = m.addVar(lb=70, ub=160, vtype=GRB.INTEGER, name="two_inch_binders")

# Set the objective function
m.setObjective(1*x1 + 2*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 >= 200, "total_binders")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"One-inch binders: {x1.x}")
    print(f"Two-inch binders: {x2.x}")
    print(f"Total profit: {m.objVal}")
else:
    print("No optimal solution found")
```