To solve the problem described, we first need to convert the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints.

Let's define:
- $x$ as the fraction of each liter that is cheap paint.
- $y$ as the fraction of each liter that is expensive paint.

The objective is to minimize the cost. The cost per liter of the mix can be calculated as $0.30x + 1.50y$. 

Given that we want a quality of at least 80, and knowing the qualities are 50 for cheap paint and 90 for expensive paint, the quality constraint can be represented as $50x + 90y \geq 80$. Since $x$ and $y$ represent fractions of a liter, we also have the constraints $x + y = 1$ (to ensure we're considering the full liter), $x \geq 0$, and $y \geq 0$.

The symbolic representation of the problem is:

```json
{
  'sym_variables': [('x', 'fraction of cheap paint'), ('y', 'fraction of expensive paint')],
  'objective_function': '0.30*x + 1.50*y',
  'constraints': ['50*x + 90*y >= 80', 'x + y == 1', 'x >= 0', 'y >= 0']
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x = m.addVar(vtype=GRB.CONTINUOUS, name="cheap_paint_fraction", lb=0)
y = m.addVar(vtype=GRB.CONTINUOUS, name="expensive_paint_fraction", lb=0)

# Objective function: minimize cost
m.setObjective(0.30*x + 1.50*y, GRB.MINIMIZE)

# Constraints
m.addConstr(50*x + 90*y >= 80, "Quality_Constraint")
m.addConstr(x + y == 1, "Total_Fraction_Constraint")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Fraction of cheap paint: {x.x}")
    print(f"Fraction of expensive paint: {y.x}")
    print(f"Minimum cost per liter: {m.objVal}")
else:
    print("No optimal solution found")
```