VRP$\_$TSP $($Python: import math

from gurobipy import GRB

import gurobipy as gp

import networkx as nx$)$

A furniture manufacturer stores fumiture in a warehouse located at coordinates $x=420$ and $Y=700,$ for weekly deliveries to warious

consumption sites. The firm operates a fleet of four trucks, each with a hauling capacity of $40000kg.$ For a apecific week, the required

deliveries are detailed in the following table.

The trucks should be scheduled to ship all orders for the week at one time, starting from the warehouse. The capacities of the trucks must not be exceeded,

and all trucks should return to the warehouse upon completion of their routes. Road distances are estimated to be $20\%$ higher than straight$-$line,

coordinate$-$computed distances. Each route incurs a fixed cost of $200$ and truck costs are $0\mathrm{.}8$ per kilometre.

Using the MILP formulation covered in the class $($which should be applied to this case and presented in the report$),$ solve the problem for the least

distance set of routes, eliminating sub$-$tours with the MTZ constraints. Calculate the vehicle capacity utilization for each route and provide comments on

the reaults. Present the final routes in a figure. $2.$ Modify the existing model to minimize cost and compare the resulting solution with the solution obtained

in question $1.$ What impact would result if the manufacturer could use less than four trucks? Rewrite the constraint that translates this change. Comment

on the results. $3.$ Consider the solution from question $1.$ Calculate the overall cost of this solution, including labour costs. Assume the following

conditions: drivers operate within two $4-$hour periods each day, separated by a $30-$minute break; the average speed is $75k\frac{m}{h}$; drivers must return to the

depot; labour is priced at $25$ C per hour $($including breaks$)$; and the overnight cost is $1406.$ Illustrate the drivers' schedule in a diagram. Tip: Optimization is

not required to answer this question. $4.$ Analyse the workload distribution among drivers based on the routes obtained from question $1.$ Propose a more

evenly balanced set of routes, calculate the overall costs for your proposed solution, and provide comments on the results. Ulustrate the proposed drivers'

achedule in a diagram. Tip: Optimization is not required to answer this question.