Here's the Gurobi code for the optimization problem:

```python
from gurobipy import Model, GRB

# Create a new model
model = Model("optimization_problem")

# Create variables
ham_sandwiches = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name="ham_sandwiches")
black_beans = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name="black_beans")
steaks = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name="steaks")
apple_pies = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name="apple_pies")
chicken_thighs = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name="chicken_thighs")
cornichons = model.addVar(lb=0, vtype=GRB.INTEGER, name="cornichons")

# Set objective function
model.setObjective(6 * ham_sandwiches * black_beans + ham_sandwiches * apple_pies + 7 * black_beans * black_beans + 5 * black_beans * steaks + 8 * black_beans * cornichons + 3 * steaks * steaks + 6 * steaks * apple_pies + 2 * steaks * cornichons + 9 * apple_pies * chicken_thighs + 4 * chicken_thighs * cornichons + 2 * cornichons * cornichons, GRB.MINIMIZE)

# Add constraints
model.addConstr(1.94 * ham_sandwiches + 3.66 * black_beans + 1.77 * steaks + 2.05 * apple_pies + 3.2 * chicken_thighs + 0.29 * cornichons <= 44, "c0")
model.addConstr(0.93 * ham_sandwiches + 2.25 * black_beans + 0.87 * steaks + 0.56 * apple_pies + 1.75 * chicken_thighs + 2.88 * cornichons <= 110, "c1")
model.addConstr(3.66 * black_beans + 2.05 * apple_pies >= 5, "c2")
model.addConstr(1.94 * ham_sandwiches + 3.2 * chicken_thighs >= 2, "c3")
model.addConstr(3.66 * black_beans * black_beans + 0.29 * cornichons * cornichons >= 3, "c4")
model.addConstr(1.94 * ham_sandwiches + 0.29 * cornichons >= 6, "c5")
model.addConstr(2.05 * apple_pies + 3.2 * chicken_thighs >= 7, "c6")
model.addConstr(3.66 * black_beans + 3.2 * chicken_thighs >= 3, "c7")
model.addConstr(1.94 * ham_sandwiches + 3.66 * black_beans + 1.77 * steaks + 2.05 * apple_pies + 3.2 * chicken_thighs + 0.29 * cornichons >= 3, "c8")
model.addConstr(2.25 * black_beans + 0.87 * steaks >= 8, "c9")
model.addConstr(2.25 * black_beans * black_beans + 1.75 * chicken_thighs * chicken_thighs >= 15, "c10")
model.addConstr(0.87 * steaks + 0.56 * apple_pies >= 8, "c11")
model.addConstr(0.56 * apple_pies + 2.88 * cornichons >= 15, "c12")
model.addConstr(0.93 * ham_sandwiches * ham_sandwiches + 0.87 * steaks * steaks >= 7, "c13")
model.addConstr(0.87 * steaks * steaks + 2.88 * cornichons * cornichons >= 16, "c14")
model.addConstr(0.93 * ham_sandwiches * ham_sandwiches + 2.88 * cornichons * cornichons >= 9, "c15")
model.addConstr(0.93 * ham_sandwiches + 2.25 * black_beans >= 7, "c16")
model.addConstr(2.25 * black_beans * black_beans + 2.88 * cornichons * cornichons >= 12, "c17")
model.addConstr(1.75 * chicken_thighs + 2.88 * cornichons >= 13, "c18")
model.addConstr(2.25 * black_beans + 0.56 * apple_pies >= 10, "c19")
model.addConstr(0.93 * ham_sandwiches + 2.25 * black_beans + 0.87 * steaks + 0.56 * apple_pies + 1.75 * chicken_thighs + 2.88 * cornichons >= 10, "c20")
model.addConstr(3 * ham_sandwiches - 9 * chicken_thighs >= 0, "c21")
# ... (rest of the constraints)


# Optimize model
model.optimize()

# Print results
if model.status == GRB.OPTIMAL:
    print('Obj: %g' % model.objVal)
    for v in model.getVars():
        print('%s %g' % (v.varName, v.x))
elif model.status == GRB.INFEASIBLE:
    print('Optimization problem is infeasible.')

```