## Problem Description and Formulation

The problem is a linear programming optimization problem where we need to minimize the cost of creating a new mixture from two different products, Omega and Omini. Each product has different costs and contains different units of water, detergent, and bleach. The new mixture must meet certain requirements for water, detergent, and bleach.

## Decision Variables

Let \(x\) be the number of cans from Omega and \(y\) be the number of cans from Omini.

## Objective Function

The objective is to minimize the total cost, which is given by \(30x + 40y\).

## Constraints

1. Water constraint: \(3x + 5y \geq 30\)
2. Detergent constraint: \(5x + 6y \geq 35\)
3. Bleach constraint: \(6x + 5y \geq 40\)
4. Non-negativity constraints: \(x \geq 0, y \geq 0\)

## Gurobi Code

```python
import gurobi

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

    # Define decision variables
    x = model.addVar(lb=0, name="Omega_cans")  # cans from Omega
    y = model.addVar(lb=0, name="Omini_cans")  # cans from Omini

    # Objective function: minimize cost
    model.setObjective(30*x + 40*y, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(3*x + 5*y >= 30, name="water_constraint")
    model.addConstr(5*x + 6*y >= 35, name="detergent_constraint")
    model.addConstr(6*x + 5*y >= 40, name="bleach_constraint")

    # Optimize
    model.optimize()

    # Solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: x = {x.varValue}, y = {y.varValue}")
        print(f"Minimum cost: {model.objVal}")
    else:
        print("No optimal solution found")

solve_laundromat_problem()
```

This code defines the optimization problem using Gurobi's Python interface, solves it, and prints out the optimal solution and the minimum cost if an optimal solution is found. If no optimal solution exists (e.g., if the problem is infeasible), it indicates that as well.