## Problem Description and Formulation

The problem is a linear programming (LP) optimization problem. We need to minimize the cost of two supplement drinks, orange flavored and apple flavored, while meeting the daily recommended intake of fiber and iron.

Let's define the decision variables:

* `x`: number of servings of orange flavored drink
* `y`: number of servings of apple flavored drink

The objective function is to minimize the total cost:

* Cost of orange flavored drink: $8 per serving
* Cost of apple flavored drink: $5 per serving

The constraints are:

* Fiber intake: at least 13 grams per day
* Iron intake: at least 13 grams per day
* Non-negativity: `x` and `y` must be non-negative (we can't have a negative number of servings)

## Mathematical Formulation

The mathematical formulation of the problem is:

Minimize: `8x + 5y`

Subject to:

* `4x + 6y >= 13` (fiber intake)
* `5x + 3y >= 13` (iron intake)
* `x >= 0` (non-negativity)
* `y >= 0` (non-negativity)

## Gurobi Code

```python
import gurobi

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

# Define the decision variables
x = model.addVar(lb=0, name="orange_servings")
y = model.addVar(lb=0, name="apple_servings")

# Define the objective function
model.setObjective(8*x + 5*y, gurobi.GRB.MINIMIZE)

# Define the constraints
fiber_constraint = model.addConstr(4*x + 6*y >= 13, name="fiber_intake")
iron_constraint = model.addConstr(5*x + 3*y >= 13, name="iron_intake")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Orange servings: {x.varValue}")
    print(f"Apple servings: {y.varValue}")
    print(f"Total cost: ${model.objVal:.2f}")
else:
    print("No optimal solution found.")
```