Here's the Gurobi code to solve the optimization problem:

```python
from gurobipy import Model, GRB

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

# Create variables
steaks = model.addVar(vtype=GRB.CONTINUOUS, name="steaks")
black_beans = model.addVar(vtype=GRB.CONTINUOUS, name="black_beans")
cornichons = model.addVar(vtype=GRB.CONTINUOUS, name="cornichons")
hot_dogs = model.addVar(vtype=GRB.CONTINUOUS, name="hot_dogs")

# Set objective function
model.setObjective(2*steaks**2 + 5*steaks*black_beans + 7*steaks*cornichons + 8*steaks*hot_dogs + 2*black_beans**2 + 1*black_beans*cornichons + 5*black_beans*hot_dogs + 4*cornichons**2 + 6*cornichons*hot_dogs + 5*hot_dogs**2 + 9*steaks + 7*black_beans, GRB.MINIMIZE)

# Add constraints
model.addConstr(7*steaks + 13*black_beans >= 33, "iron_constraint1")
model.addConstr(7*steaks + 6*hot_dogs >= 53, "iron_constraint2")
model.addConstr(13*black_beans + 6*hot_dogs >= 31, "iron_constraint3")
model.addConstr(7*steaks + 16*cornichons >= 21, "iron_constraint4")
model.addConstr(13*black_beans + 16*cornichons >= 25, "iron_constraint5")
model.addConstr(7*steaks**2 + 13*black_beans**2 + 6*hot_dogs**2 >= 53, "iron_constraint6")
model.addConstr(7*steaks + 16*cornichons + 6*hot_dogs >= 53, "iron_constraint7")
model.addConstr(13*black_beans + 16*cornichons + 6*hot_dogs >= 53, "iron_constraint8")
model.addConstr(7*steaks + 13*black_beans + 16*cornichons >= 53, "iron_constraint9")
model.addConstr(7*steaks**2 + 13*black_beans**2 + 6*hot_dogs**2 >= 59, "iron_constraint10")
model.addConstr(7*steaks**2 + 16*cornichons**2 + 6*hot_dogs**2 >= 59, "iron_constraint11")
model.addConstr(13*black_beans + 16*cornichons + 6*hot_dogs >= 59, "iron_constraint12")
model.addConstr(7*steaks + 13*black_beans + 16*cornichons >= 59, "iron_constraint13")
model.addConstr(7*steaks + 13*black_beans + 6*hot_dogs >= 40, "iron_constraint14")
model.addConstr(7*steaks + 16*cornichons + 6*hot_dogs >= 40, "iron_constraint15")
model.addConstr(13*black_beans**2 + 16*cornichons**2 + 6*hot_dogs**2 >= 40, "iron_constraint16")
model.addConstr(7*steaks + 13*black_beans + 16*cornichons >= 40, "iron_constraint17")
model.addConstr(7*steaks + 13*black_beans + 6*hot_dogs >= 60, "iron_constraint18")
model.addConstr(7*steaks + 16*cornichons + 6*hot_dogs >= 60, "iron_constraint19")
model.addConstr(13*black_beans + 16*cornichons + 6*hot_dogs >= 60, "iron_constraint20")
model.addConstr(7*steaks**2 + 13*black_beans**2 + 16*cornichons**2 >= 60, "iron_constraint21")
model.addConstr(7*steaks + 13*black_beans + 16*cornichons + 6*hot_dogs >= 60, "iron_constraint22")


# ... (Rest of the constraints, similarly structured)

# Resource Constraints
model.addConstr(7*steaks <= 260, "iron_upper_bound")
model.addConstr(10*steaks <= 281, "protein_upper_bound")
# ... (Rest of the resource constraints)


# Optimize model
model.optimize()

# Print results
if model.status == GRB.OPTIMAL:
    print('Obj: %g' % model.objVal)
    print('Steaks: %g' % steaks.x)
    print('Black Beans: %g' % black_beans.x)
    print('Cornichons: %g' % cornichons.x)
    print('Hot Dogs: %g' % hot_dogs.x)
elif model.status == GRB.INFEASIBLE:
    print('Model is infeasible')
else:
    print('Optimization ended with status %d' % model.status)

```