## Problem Description and Formulation

The problem is a classic example of a linear programming problem. Mia Clothing wants to maximize profit by determining the optimal weekly production of skirts and coats, given the constraints on the available hours of the sewing machine and embroidery machine.

Let's define the decision variables:
- \(x\): the number of skirts produced per week
- \(y\): the number of coats produced per week

The objective function to maximize profit is:
\[ \text{Maximize:} \quad 300x + 500y \]

The constraints based on the available machine hours are:
- Sewing machine: \(3x + 2y \leq 25\)
- Embroidery machine: \(5x + 3.5y \leq 35\)

Additionally, \(x \geq 0\) and \(y \geq 0\), since the number of skirts and coats produced cannot be negative.

## Gurobi Code

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

```python
import gurobi

def solve_production_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the decision variables
    x = model.addVar(lb=0, name="Skirts")
    y = model.addVar(lb=0, name="Coats")

    # Objective function: Maximize profit
    model.setObjective(300*x + 500*y, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(3*x + 2*y <= 25, name="Sewing_Machine_Constraint")
    model.addConstr(5*x + 3.5*y <= 35, name="Embroidery_Machine_Constraint")

    # Optimize the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal production levels:")
        print(f"Skirts: {x.varValue}")
        print(f"Coats: {y.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("The model is infeasible")

solve_production_problem()
```

This code defines the problem in a way that Gurobi can understand and solve it. It sets up the decision variables, the objective function, and the constraints, and then calls Gurobi's solver to find the optimal solution. If the model is feasible, it prints out the optimal production levels for skirts and coats and the maximum achievable profit.