To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's denote the number of cans of Ruby paint as \(x_1\) and the number of cans of Sapphire paint as \(x_2\).

The objective is to minimize the total cost, which can be represented as \(12x_1 + 15x_2\), since a can of Ruby paint costs $12 and a can of Sapphire paint costs $15.

The constraints are based on the minimum requirements of dye, thinner, and water for the new mixture:
- Dye: \(2x_1 + 4x_2 \geq 15\)
- Thinner: \(4x_1 + 6x_2 \geq 20\)
- Water: \(5x_1 + 2x_2 \geq 18\)

Also, \(x_1 \geq 0\) and \(x_2 \geq 0\) because the number of cans cannot be negative.

The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of cans of Ruby paint'), ('x2', 'number of cans of Sapphire paint')],
    'objective_function': '12*x1 + 15*x2',
    'constraints': [
        '2*x1 + 4*x2 >= 15',
        '4*x1 + 6*x2 >= 20',
        '5*x1 + 2*x2 >= 18',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

To solve this problem using Gurobi in Python, we'll use the following code:
```python
from gurobipy import *

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

# Create variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="Ruby_Paint")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="Sapphire_Paint")

# Set the objective function
m.setObjective(12*x1 + 15*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(2*x1 + 4*x2 >= 15, "Dye_Requirement")
m.addConstr(4*x1 + 6*x2 >= 20, "Thinner_Requirement")
m.addConstr(5*x1 + 2*x2 >= 18, "Water_Requirement")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of cans of Ruby paint: {x1.x}")
    print(f"Number of cans of Sapphire paint: {x2.x}")
    print(f"Total cost: ${12*x1.x + 15*x2.x:.2f}")
else:
    print("No optimal solution found")
```