## Problem Description and Formulation

The problem described is a classic example of a linear programming problem, specifically a diet problem. The goal is to determine the optimal amount of each food to consume daily to meet the macronutrient requirements at the minimum cost.

Let's denote:
- $F$ as the set of available foods,
- $M$ as the set of macronutrients,
- $c_f$ as the cost per serving of food $f \in F$,
- $a_{mf}$ as the amount of macronutrient $m \in M$ in one serving of food $f \in F$,
- $b_m$ as the required daily amount of macronutrient $m \in M$,
- $x_f$ as the number of servings of food $f \in F$ to consume daily.

The problem can be formulated as:

Minimize:
\[ \sum_{f \in F} c_f x_f \]

Subject to:
\[ \sum_{f \in F} a_{mf} x_f \geq b_m \quad \forall m \in M \]
\[ x_f \geq 0 \quad \forall f \in F \]

## Applying to the Given Data

Given:
- Foods: Rice ($R$), Beef ($B$)
- Macronutrients: Protein ($P$), Carbs ($C$), Fat ($F$)
- Cost per serving: $c_R = 5$, $c_B = 30$
- Macronutrient content per serving:
  - $a_{PR} = 2$, $a_{PB} = 20$
  - $a_{CR} = 80$, $a_{CB} = 200$
  - $a_{FR} = 1$, $a_{FB} = 16$
- Required daily amounts:
  - $b_P = 50$, $b_C = 1000$, $b_F = 40$

## Gurobi Code

```python
import gurobi

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

    # Define sets
    foods = ['Rice', 'Beef']
    macronutrients = ['Protein', 'Carbs', 'Fat']

    # Define parameters
    cost = {'Rice': 5, 'Beef': 30}
    nutrient_content = {
        'Protein': {'Rice': 2, 'Beef': 20},
        'Carbs': {'Rice': 80, 'Beef': 200},
        'Fat': {'Rice': 1, 'Beef': 16}
    }
    requirements = {'Protein': 50, 'Carbs': 1000, 'Fat': 40}

    # Create variables
    x = {}
    for food in foods:
        x[food] = model.addVar(name=food, lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Objective function: minimize cost
    model.setObjective(gurobi.quicksum([cost[food] * x[food] for food in foods]), gurobi.GRB.MINIMIZE)

    # Constraints: meet nutrient requirements
    for nutrient, requirement in requirements.items():
        model.addConstr(gurobi.quicksum([nutrient_content[nutrient][food] * x[food] for food in foods]) >= requirement, name=nutrient)

    # Solve the model
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal servings:")
        for food in foods:
            print(f"{food}: {x[food].x:.2f}")
        print(f"Optimal cost: {model.objVal:.2f}")
    else:
        print("No optimal solution found.")

# Run the model
diet_problem()
```