## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The goal is to minimize the cost of dog food while ensuring the puppy gets at least 30 units of minerals and 40 units of vitamins.

Let's define the decision variables:

* `x`: number of servings of dog food A
* `y`: number of servings of dog food B

The objective function is to minimize the total cost:

* `3x + 5y`: total cost

The constraints are:

* `4x + 8y >= 30`: total minerals
* `5x + 2y >= 40`: total vitamins
* `x >= 0`, `y >= 0`: non-negativity constraints (cannot buy negative servings)

## Gurobi Code

```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the decision variables
x = model.addVar(lb=0, name="x")  # servings of dog food A
y = model.addVar(lb=0, name="y")  # servings of dog food B

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

# Define the constraints
model.addConstr(4*x + 8*y >= 30, name="minerals")
model.addConstr(5*x + 2*y >= 40, name="vitamins")

# Optimize the model
model.optimize()

# Print the results
if model.status == gurobi.OPTIMAL:
    print("Optimal solution found.")
    print(f"Servings of dog food A: {x.varValue}")
    print(f"Servings of dog food B: {y.varValue}")
    print(f"Total cost: ${model.objVal:.2f}")
else:
    print("No optimal solution found.")
```

This code defines the decision variables, objective function, and constraints, and then solves the model using Gurobi's optimization algorithm. If an optimal solution is found, it prints the number of servings of each dog food and the total cost. If no optimal solution is found, it indicates that the problem is infeasible.