Here's the formulation of the linear program and the Gurobi code to solve it:

**Decision Variables:**

* `x`: Number of one-inch binders produced.
* `y`: Number of two-inch binders produced.

**Objective Function:**

Maximize profit: `z = 1x + 2y`

**Constraints:**

* Demand for one-inch binders: `x >= 60`
* Demand for two-inch binders: `y >= 70`
* Production capacity for one-inch binders: `x <= 150`
* Production capacity for two-inch binders: `y <= 160`
* Total binder contract: `x + y >= 200`
* Non-negativity: `x, y >= 0`


```python
import gurobipy as gp
from gurobipy import GRB

# Create a new model
model = gp.Model("binder_production")

# Create decision variables
x = model.addVar(lb=0, vtype=GRB.INTEGER, name="one_inch_binders")
y = model.addVar(lb=0, vtype=GRB.INTEGER, name="two_inch_binders")

# Set objective function
model.setObjective(1*x + 2*y, GRB.MAXIMIZE)

# Add constraints
model.addConstr(x >= 60, "demand_one_inch")
model.addConstr(y >= 70, "demand_two_inch")
model.addConstr(x <= 150, "capacity_one_inch")
model.addConstr(y <= 160, "capacity_two_inch")
model.addConstr(x + y >= 200, "total_binders")

# Optimize model
model.optimize()

# Print results
if model.status == GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"Number of one-inch binders: {x.x}")
    print(f"Number of two-inch binders: {y.x}")
    print(f"Maximum Profit: ${model.objVal}")
elif model.status == GRB.INFEASIBLE:
    print("Model is infeasible.")
else:
    print(f"Optimization terminated with status: {model.status}")

```
