## Step 1: Define the symbolic representation of the problem

Let's denote the number of servings of dog food A as $x_1$ and the number of servings of dog food B as $x_2$. The objective is to minimize the cost, which is $3x_1 + 5x_2$. The constraints are:

- $4x_1 + 8x_2 \geq 30$ (at least 30 units of minerals)
- $5x_1 + 2x_2 \geq 40$ (at least 40 units of vitamins)
- $x_1 \geq 0$ and $x_2 \geq 0$ (non-negativity constraints, as the number of servings cannot be negative)

## Step 2: Express the problem in the required symbolic format

The symbolic variables are:
- $x_1$ for servings of dog food A
- $x_2$ for servings of dog food B

The objective function is: $3x_1 + 5x_2$

The constraints are:
- $4x_1 + 8x_2 \geq 30$
- $5x_1 + 2x_2 \geq 40$
- $x_1 \geq 0$
- $x_2 \geq 0$

In the required format:
```json
{
'sym_variables': [('x1', 'servings of dog food A'), ('x2', 'servings of dog food B')],
'objective_function': '3*x1 + 5*x2',
'constraints': ['4*x1 + 8*x2 >= 30', '5*x1 + 2*x2 >= 40', 'x1 >= 0', 'x2 >= 0']
}
```

## Step 3: Convert the problem into Gurobi code

To solve this linear programming problem using Gurobi, we will use the Gurobi Python API.

```python
import gurobi

def solve_dog_food_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="dog_food_A", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name="dog_food_B", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Define the objective function
    model.setObjective(3*x1 + 5*x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(4*x1 + 8*x2 >= 30, name="minerals_constraint")
    model.addConstr(5*x1 + 2*x2 >= 40, name="vitamins_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Servings of dog food A: {x1.varValue}")
        print(f"Servings of dog food B: {x2.varValue}")
        print(f"Total cost: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_dog_food_problem()
```