## Problem Description and Formulation

The young man needs to meet his daily requirements of biotin and folate by consuming carrots and spinach. The goal is to minimize the cost of consumption while meeting these nutritional requirements.

### Define the Variables

- Let \(x\) be the number of cups of carrots consumed.
- Let \(y\) be the number of cups of spinach consumed.

### Define the Objective Function

The objective is to minimize the total cost of carrots and spinach. Given that the cost per cup of carrots is $5 and the cost per cup of spinach is $3, the objective function can be formulated as:

\[ \text{Minimize:} \quad 5x + 3y \]

### Define the Constraints

1. **Biotin Requirement:** One cup of carrots contains 1 gram of biotin, and one cup of spinach contains 2 grams of biotin. The requirement is at least 20 grams of biotin per day.

\[ x + 2y \geq 20 \]

2. **Folate Requirement:** One cup of carrots contains 3 grams of folate, and one cup of spinach contains 1.5 grams of folate. The requirement is at least 20 grams of folate per day.

\[ 3x + 1.5y \geq 20 \]

3. **Non-Negativity Constraints:** The number of cups of carrots and spinach consumed cannot be negative.

\[ x \geq 0, \quad y \geq 0 \]

## Gurobi Code

```python
import gurobi

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

    # Define the variables
    x = model.addVar(lb=0, name="carrots")  # cups of carrots
    y = model.addVar(lb=0, name="spinach")  # cups of spinach

    # Define the objective function
    model.setObjective(5*x + 3*y, gurobi.GRB.MINIMIZE)

    # Add biotin requirement constraint
    model.addConstr(x + 2*y >= 20, name="biotin_requirement")

    # Add folate requirement constraint
    model.addConstr(3*x + 1.5*y >= 20, name="folate_requirement")

    # Optimize the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution found. Carrots: {x.varValue}, Spinach: {y.varValue}")
    else:
        print("No optimal solution found.")

# Run the optimization problem
solve_optimization_problem()
```

This Gurobi code defines the optimization problem as described, with the objective to minimize the cost of consuming carrots and spinach while meeting the biotin and folate requirements. It then solves the problem and prints out the optimal consumption levels if a solution is found.