To solve this optimization problem using Gurobi, we will first define the variables and their types based on the given constraints. Then, we'll formulate the objective function and the constraints according to the problem description.

Given:
- Variables: `strips_of_bacon`, `cherry_pies`, `slices_of_pizza`, `bagged_salads`, `peanutbutter_sandwiches`
- Objective Function: Minimize `3.17 * strips_of_bacon + 8.18 * cherry_pies + 6.91 * slices_of_pizza + 8.42 * bagged_salads + 4.16 * peanutbutter_sandwiches`
- Constraints:
  - Cost constraints for each item
  - Lower bound constraints on combinations of items
  - Upper bound constraints on combinations of items
  - Variable type constraints (integer, continuous)

The reasoning behind the formulation is to directly translate the problem description into mathematical expressions that Gurobi can solve. We will use `GRB.CONTINUOUS` for variables that can be fractional and `GRB.INTEGER` for those that must be whole numbers.

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define the variables
strips_of_bacon = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="strips_of_bacon")
cherry_pies = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="cherry_pies")
slices_of_pizza = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.INTEGER, name="slices_of_pizza")
bagged_salads = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="bagged_salads")
peanutbutter_sandwiches = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.INTEGER, name="peanutbutter_sandwiches")

# Define the objective function
m.setObjective(3.17 * strips_of_bacon + 8.18 * cherry_pies + 6.91 * slices_of_pizza + 8.42 * bagged_salads + 4.16 * peanutbutter_sandwiches, GRB.MINIMIZE)

# Define the constraints
m.addConstr(9 * strips_of_bacon + 8 * cherry_pies >= 27, name="constraint_1")
m.addConstr(9 * strips_of_bacon + 12 * peanutbutter_sandwiches >= 53, name="constraint_2")
m.addConstr(6 * bagged_salads + 12 * peanutbutter_sandwiches >= 35, name="constraint_3")
m.addConstr(10 * slices_of_pizza + 12 * peanutbutter_sandwiches >= 40, name="constraint_4")
m.addConstr(8 * cherry_pies + 12 * peanutbutter_sandwiches >= 66, name="constraint_5")
m.addConstr(9 * strips_of_bacon + 8 * cherry_pies + 10 * slices_of_pizza + 6 * bagged_salads + 12 * peanutbutter_sandwiches >= 66, name="constraint_6")
m.addConstr(9 * strips_of_bacon + 8 * cherry_pies <= 143, name="constraint_7")
m.addConstr(8 * cherry_pies + 6 * bagged_salads <= 254, name="constraint_8")
m.addConstr(8 * cherry_pies + 6 * bagged_salads + 12 * peanutbutter_sandwiches <= 110, name="constraint_9")

# Optimize the model
m.optimize()

```