## Problem Description and Formulation

The problem is an optimization problem where we need to maximize an objective function subject to several constraints. The objective function is to maximize \(1.24 \times \text{green beans} + 3.93 \times \text{ham sandwiches} + 1.9 \times \text{cornichons}\).

The constraints are as follows:
- The cost of green beans is $6 each, ham sandwiches are $15 each, and cornichons are $4 each.
- The fiber content of green beans is 10 grams each, ham sandwiches are 16 grams each, and cornichons are 1 gram each.
- Minimum spend on green beans and ham sandwiches is $42.
- Minimum spend on ham sandwiches and cornichons is $33.
- Minimum total spend on all items is $34.
- Maximum spend on green beans and ham sandwiches is $72.
- Maximum total spend on all items is $72.
- Maximum fiber from ham sandwiches and cornichons is 122 grams.
- Maximum fiber from green beans and ham sandwiches is 70 grams.
- Maximum total fiber from all items is 70 grams.
- The quantities of green beans, ham sandwiches, and cornichons can be fractional.

## Gurobi Code Formulation

```python
import gurobi

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

    # Define variables
    green_beans = model.addVar(name="green_beans", lb=0)
    ham_sandwiches = model.addVar(name="ham_sandwiches", lb=0)
    cornichons = model.addVar(name="cornichons", lb=0)

    # Objective function
    model.setObjective(1.24 * green_beans + 3.93 * ham_sandwiches + 1.9 * cornichons, gurobi.GRB.MAXIMIZE)

    # Constraints
    # Cost constraints
    model.addConstr(6 * green_beans + 15 * ham_sandwiches >= 42, name="min_spend_green_beans_ham")
    model.addConstr(15 * ham_sandwiches + 4 * cornichons >= 33, name="min_spend_ham_cornichons")
    model.addConstr(6 * green_beans + 15 * ham_sandwiches + 4 * cornichons >= 34, name="min_total_spend")
    model.addConstr(6 * green_beans + 15 * ham_sandwiches <= 72, name="max_spend_green_beans_ham")
    model.addConstr(6 * green_beans + 15 * ham_sandwiches + 4 * cornichons <= 72, name="max_total_spend")

    # Fiber constraints
    model.addConstr(16 * ham_sandwiches + cornichons <= 122, name="max_fiber_ham_cornichons")
    model.addConstr(10 * green_beans + 16 * ham_sandwiches <= 70, name="max_fiber_green_beans_ham")
    model.addConstr(10 * green_beans + 16 * ham_sandwiches + cornichons <= 70, name="max_total_fiber")

    # Solve the problem
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Green Beans: {green_beans.varValue}")
        print(f"Ham Sandwiches: {ham_sandwiches.varValue}")
        print(f"Cornichons: {cornichons.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("The problem is infeasible")

optimize_problem()
```