To solve the given problem, we first need to convert the natural language description into a symbolic representation. Let's denote:

- $x_1$ as the number of servings of dog food A
- $x_2$ as the number of servings of dog food B

The objective is to minimize the total cost. The cost of dog food A per serving is $3, and the cost of dog food B per serving is $5. Thus, the objective function can be represented as:

\[ \text{Minimize:} \quad 3x_1 + 5x_2 \]

The constraints are:
1. The puppy must get at least 30 units of minerals. Given that a serving of dog food A contains 4 units of minerals and a serving of dog food B contains 8 units of minerals, we have:

\[ 4x_1 + 8x_2 \geq 30 \]

2. The puppy must get at least 40 units of vitamins. Since a serving of dog food A contains 5 units of vitamins and a serving of dog food B contains 2 units of vitamins, we have:

\[ 5x_1 + 2x_2 \geq 40 \]

3. Non-negativity constraints: The number of servings cannot be negative.

\[ x_1 \geq 0, \quad x_2 \geq 0 \]

Therefore, the symbolic representation of the problem is:

```json
{
  'sym_variables': [('x1', 'number of servings of dog food A'), ('x2', 'number of 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']
}
```

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

```python
from gurobipy import *

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

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

# Set the objective function
m.setObjective(3*x1 + 5*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(4*x1 + 8*x2 >= 30, name="minerals")
m.addConstr(5*x1 + 2*x2 >= 40, name="vitamins")

# Optimize model
m.optimize()

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