To solve this optimization problem, we need to define the decision variables, objective function, and constraints. Let's denote the number of servings of dog food A as x and the number of servings of dog food B as y.

The objective is to minimize the total cost, which can be represented by the equation: 3x + 5y.

We have two constraints based on the requirements for minerals and vitamins:
1. The puppy should get at least 30 units of minerals: 4x + 8y ≥ 30.
2. The puppy should get at least 40 units of vitamins: 5x + 2y ≥ 40.

Additionally, x and y must be non-negative since we cannot buy a negative number of servings.

Here is the Gurobi code that solves this problem:

```python
from gurobipy import *

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

# Define the decision variables
x = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="dog_food_A")
y = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="dog_food_B")

# Define the objective function
m.setObjective(3*x + 5*y, GRB.MINIMIZE)

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

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print("Servings of dog food A:", x.x)
    print("Servings of dog food B:", y.x)
    print("Total cost: $", 3*x.x + 5*y.x)
else:
    print("No optimal solution found. The problem is infeasible.")

```