To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables and translating the constraints and objective function into algebraic terms.

Let's denote:
- \(x_1\) as the amount of Mix A (in kg) that the breakfast place should buy.
- \(x_2\) as the amount of Mix B (in kg) that the breakfast place should buy.

The objective is to minimize the total cost, which can be represented by the objective function:
\[ \text{Minimize} \quad 20x_1 + 25x_2 \]

Given the constraints:
- The final mixture needs at least 10 kg of sugar. Since Mix A contains 10% sugar and Mix B contains 15% sugar, this translates to \(0.10x_1 + 0.15x_2 \geq 10\).
- The final mixture needs at least 50 kg of flour. With Mix A containing 60% flour and Mix B containing 50% flour, we have \(0.60x_1 + 0.50x_2 \geq 50\).

Additionally, since the breakfast place cannot buy a negative amount of any mix, we also have:
- \(x_1 \geq 0\)
- \(x_2 \geq 0\)

Thus, the symbolic representation of the problem can be summarized as:

```json
{
  'sym_variables': [('x1', 'amount of Mix A in kg'), ('x2', 'amount of Mix B in kg')],
  'objective_function': '20*x1 + 25*x2',
  'constraints': ['0.10*x1 + 0.15*x2 >= 10', '0.60*x1 + 0.50*x2 >= 50', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this optimization problem using Gurobi in Python, we use the following code:

```python
from gurobipy import *

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

# Create variables
x1 = m.addVar(lb=0, name="Mix_A")
x2 = m.addVar(lb=0, name="Mix_B")

# Set the objective function
m.setObjective(20*x1 + 25*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(0.10*x1 + 0.15*x2 >= 10, "Sugar_Constraint")
m.addConstr(0.60*x1 + 0.50*x2 >= 50, "Flour_Constraint")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Buy {x1.x} kg of Mix A")
    print(f"Buy {x2.x} kg of Mix B")
    print(f"Total cost: ${20*x1.x + 25*x2.x}")
else:
    print("No optimal solution found")
```