## Problem Description and Formulation

The problem is a linear programming optimization problem. Northwest Golden Bakery wants to minimize the cost of making cakes with chocolate and strawberry toppings. The toppings have specific sugar and butter requirements, and there are limits on the number of chocolate toppings.

### Decision Variables

- Let \(C\) be the number of chocolate toppings.
- Let \(S\) be the number of strawberry toppings.

### Objective Function

The objective is to minimize the total cost. It costs $2 to make one chocolate topping and $3 for one strawberry topping. Therefore, the objective function is:

\[ \text{Minimize:} \quad 2C + 3S \]

### Constraints

1. **Sugar Constraint:** Each chocolate topping contains 1 gram of sugar, and each strawberry topping contains 0.5 grams of sugar. The cake must have at least 10 grams of sugar in the toppings.

\[ 1C + 0.5S \geq 10 \]

2. **Butter Constraint:** Each chocolate topping contains 2 grams of butter, and each strawberry topping contains 0.7 grams of butter. The cake must have at least 15 grams of butter in the toppings.

\[ 2C + 0.7S \geq 15 \]

3. **Chocolate Toppings Limit:** For health reasons, the cake will have at most 5 chocolate toppings.

\[ C \leq 5 \]

4. **Non-Negativity Constraints:** The number of toppings cannot be negative.

\[ C \geq 0, S \geq 0 \]
\[ C, S \in \mathbb{Z} \] (Implicitly, as they represent the number of toppings)

However, since Gurobi can handle continuous variables, we will first solve it as a linear program and then consider if integer constraints are needed.

## Gurobi Code

```python
import gurobi

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

    # Define variables
    C = model.addVar(lb=0, name="Chocolate_Toppings")
    S = model.addVar(lb=0, name="Strawberry_Toppings")

    # Objective function: Minimize cost
    model.setObjective(2*C + 3*S, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(C + 0.5*S >= 10, name="Sugar_Constraint")
    model.addConstr(2*C + 0.7*S >= 15, name="Butter_Constraint")
    model.addConstr(C <= 5, name="Chocolate_Toppings_Limit")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Chocolate Toppings: {C.varValue}")
        print(f"Strawberry Toppings: {S.varValue}")
        print(f"Cost: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_bakery_problem()
```

## Note on Integer Constraints

The problem implicitly requires \(C\) and \(S\) to be integers since they represent the number of toppings. The provided Gurobi code initially treats these variables as continuous. If an integer solution is strictly required, you would need to add:

```python
C = model.addVar(lb=0, type=gurobi.GRB.INTEGER, name="Chocolate_Toppings")
S = model.addVar(lb=0, type=gurobi.GRB.INTEGER, name="Strawberry_Toppings")
```

And ensure the model is solved with an appropriate method that can handle integer constraints, such as the MIP (Mixed-Integer Programming) solver. The rest of the code remains the same. 

However, note that adding integer constraints can significantly increase the problem's complexity and solving time.