To solve John's problem, we first need to define the decision variables, parameters, and constraints of the optimization model. Let's denote:

- \(x_r\) as the number of servings of rice per day,
- \(x_b\) as the number of servings of beef per day.

The given parameters are:
- Protein content in rice: 2 units/serving
- Carbs content in rice: 80 units/serving
- Fat content in rice: 1 unit/serving
- Cost of rice per serving: $5
- Protein content in beef: 20 units/serving
- Carbs content in beef: 200 units/serving
- Fat content in beef: 16 units/serving
- Cost of beef per serving: $30
- Minimum required protein: 50 units/day
- Minimum required carbs: 1000 units/day
- Minimum required fat: 40 units/day

The objective is to minimize the total cost, which can be formulated as \(5x_r + 30x_b\).

The constraints based on the macronutrient requirements are:
1. Protein requirement: \(2x_r + 20x_b \geq 50\)
2. Carbs requirement: \(80x_r + 200x_b \geq 1000\)
3. Fat requirement: \(x_r + 16x_b \geq 40\)

Also, since the number of servings cannot be negative:
4. Non-negativity constraint: \(x_r \geq 0\) and \(x_b \geq 0\).

Now, let's translate this into Gurobi code in Python:

```python
from gurobipy import *

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

# Define the decision variables
x_r = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="rice_servings")
x_b = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="beef_servings")

# Set the objective function (minimize cost)
m.setObjective(5*x_r + 30*x_b, GRB.MINIMIZE)

# Add constraints
m.addConstr(2*x_r + 20*x_b >= 50, "protein_requirement")
m.addConstr(80*x_r + 200*x_b >= 1000, "carbs_requirement")
m.addConstr(x_r + 16*x_b >= 40, "fat_requirement")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Rice servings: {x_r.x}")
    print(f"Beef servings: {x_b.x}")
    print(f"Total cost: ${5*x_r.x + 30*x_b.x:.2f}")
else:
    print("No optimal solution found")
```