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

**Decision Variables:**

* `x`: Number of lumbers produced
* `y`: Number of plywood produced

**Objective Function:**

Maximize profit: `10x + 35y`

**Constraints:**

* Worker-hours constraint: `3x + 2y <= 2500`
* Machine-hours constraint: `8x + 12y <= 4000`
* Minimum lumber constraint: `x >= 200`
* Minimum plywood constraint: `y >= 300`
* Non-negativity constraints: `x >= 0`, `y >= 0`


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

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

# Create decision variables
x = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name="lumbers")
y = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name="plywood")

# Set objective function
model.setObjective(10*x + 35*y, GRB.MAXIMIZE)

# Add constraints
model.addConstr(3*x + 2*y <= 2500, "worker_hours")
model.addConstr(8*x + 12*y <= 4000, "machine_hours")
model.addConstr(x >= 200, "min_lumbers")
model.addConstr(y >= 300, "min_plywood")

# Optimize model
model.optimize()

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

```
