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

**Decision Variables:**

* `x`: Number of coats to produce
* `y`: Number of shirts to produce

**Objective Function:**

Maximize profit:  `6x + 11y`

**Constraints:**

* Measuring: `0.7x + 0.2y <= 50`
* Cutting: `0.5x + 0.3y <= 35`
* Sewing: `0.9x + 0.5y <= 40`
* Non-negativity: `x >= 0`, `y >= 0`


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

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

# Create variables
x = m.addVar(vtype=GRB.CONTINUOUS, name="coats")  # Number of coats
y = m.addVar(vtype=GRB.CONTINUOUS, name="shirts") # Number of shirts

# Set objective function
m.setObjective(6*x + 11*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(0.7*x + 0.2*y <= 50, "measuring")
m.addConstr(0.5*x + 0.3*y <= 35, "cutting")
m.addConstr(0.9*x + 0.5*y <= 40, "sewing")

# Optimize model
m.optimize()

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

```
