To solve this problem, we first need to define the variables and the objective function. Let's denote the number of cans from Omega as $x$ and the number of cans from Omini as $y$. The objective is to minimize the total cost, which can be represented as $30x + 40y$.

The constraints are based on the contents of each can and the requirements for the new mixture:
- Water: $3x + 5y \geq 30$
- Detergent: $5x + 6y \geq 35$
- Bleach: $6x + 5y \geq 40$

Additionally, since we cannot have a negative number of cans, $x \geq 0$ and $y \geq 0$.

Now, let's translate this into Gurobi code in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Laundromat_Mixture")

# Define the variables
x = m.addVar(vtype=GRB.CONTINUOUS, name="Omega_cans", lb=0)
y = m.addVar(vtype=GRB.CONTINUOUS, name="Omini_cans", lb=0)

# Define the objective function
m.setObjective(30*x + 40*y, GRB.MINIMIZE)

# Add the constraints
m.addConstr(3*x + 5*y >= 30, "Water_constraint")
m.addConstr(5*x + 6*y >= 35, "Detergent_constraint")
m.addConstr(6*x + 5*y >= 40, "Bleach_constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: {x.varName} = {x.x}, {y.varName} = {y.x}")
    print(f"Minimum cost: {m.objVal}")
else:
    print("No optimal solution found")
```