## Step 1: Define the symbolic representation of the problem
Let's denote the fraction of Egret paint as $x$ and the fraction of Crane paint as $y$. The quality rating of Egret paint is 60 and that of Crane paint is 85. The cost of Egret paint is $0.40 per liter and that of Crane paint is $1.20 per liter. Bob wants a mix with a quality rating of at least 70.

## Step 2: Formulate the objective function and constraints
The objective is to minimize the cost, which can be represented as $0.40x + 1.20y$. The constraints are:
1. The total fraction of paint must be 1: $x + y = 1$
2. The quality rating of the mix must be at least 70: $60x + 85y \geq 70$
3. The fractions of Egret and Crane paint must be non-negative: $x \geq 0, y \geq 0$

## 3: Symbolic representation
The symbolic variables are:
- $x$ for the fraction of Egret paint
- $y$ for the fraction of Crane paint

The objective function is: $0.40x + 1.20y$

The constraints are:
- $x + y = 1$
- $60x + 85y \geq 70$
- $x \geq 0$
- $y \geq 0$

In a more formal symbolic notation as requested:
```json
{
'sym_variables': [('x', 'fraction of Egret paint'), ('y', 'fraction of Crane paint')],
'objective_function': '0.40x + 1.20y',
'constraints': ['x + y = 1', '60x + 85y >= 70', 'x >= 0', 'y >= 0']
}
```

## 4: Convert to Gurobi code in Python
```python
import gurobipy as gp

# Create a new model
model = gp.Model("Paint_Blend")

# Define the variables
x = model.addVar(name="Egret", lb=0, ub=1)  # fraction of Egret paint
y = model.addVar(name="Crane", lb=0, ub=1)  # fraction of Crane paint

# Objective function: minimize cost
model.setObjective(0.40 * x + 1.20 * y, gp.GRB.MINIMIZE)

# Constraints
model.addConstr(x + y == 1, name="Total_Fraction")  # total fraction equals 1
model.addConstr(60 * x + 85 * y >= 70, name="Quality_Rating")  # quality rating at least 70

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Fraction of Egret paint: {x.varValue}")
    print(f"Fraction of Crane paint: {y.varValue}")
    print(f"Minimum Cost: {model.objVal}")
else:
    print("No optimal solution found.")
```