## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The man wants to meet his calorie and protein requirements by eating burgers and fries at minimum cost.

Let's define the decision variables:
- \(B\): the number of burgers
- \(F\): the number of orders of fries

The objective is to minimize the total cost, which is $7 per burger and $3 per order of fries. So, the objective function is:

\[ \text{Minimize:} \quad 7B + 3F \]

Subject to the following constraints:
1. Calorie requirement: \( 500B + 300F \geq 3000 \)
2. Protein requirement: \( 30B + 5F \geq 150 \)
3. Non-negativity constraints: \( B \geq 0, F \geq 0 \)

## Gurobi Code

To solve this problem using Gurobi in Python, we will use the Gurobi Python interface. First, ensure you have Gurobi installed in your Python environment. You can install it via pip:

```bash
pip install gurobi
```

Here's the Gurobi code for the problem:

```python
import gurobi as gp

# Create a new model
m = gp.Model("diet_problem")

# Define the decision variables
B = m.addVar(name="burgers", lb=0, vtype=gp.GRB.CONTINUOUS)
F = m.addVar(name="fries", lb=0, vtype=gp.GRB.CONTINUOUS)

# Objective function: minimize cost
m.setObjective(7*B + 3*F, gp.GRB.MINIMIZE)

# Calorie requirement constraint
m.addConstr(500*B + 300*F >= 3000, name="calories")

# Protein requirement constraint
m.addConstr(30*B + 5*F >= 150, name="protein")

# Optimize the model
m.optimize()

# Print the results
if m.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution found. Cost: ${m.objVal:.2f}")
    print(f"Burgers: {B.varValue:.2f}")
    print(f"Fries: {F.varValue:.2f}")
else:
    print("No optimal solution found.")
```

This code defines the model, sets up the objective function and constraints, and then solves the optimization problem. If an optimal solution is found, it prints out the minimum cost and the quantities of burgers and fries to achieve this cost.