Fuente de Vida distributes bottled water in Tegucigalpa. The company serves customers from the traditional

$($

mom & pop stores, kiosks, small restaurants, etc.

$)$

$$and modern channel

$($

convenience stores and supermarkets

$)$

$.$

$$Fuente de Vida uses different type of vehicles for their last mile operations.

Ruby Gonzalez is in charge of last mile distribution at Fuente de Vida. She is analyzing to deploy electric cargo bikes

$($

e

$-$

bikes

$)$

$$for their delivery operations in downtown. The characteristics and delivery conditions of downtown are such that e

$-$

bikes make a lot of sense. However, further analysis is required to assess their convenience from an economical point of view. For this purpose, Ruby would like to determine the total delivery cost that would be incurred using these new electric vehicles.

She divided downtown in

$6$

$$delivery territories or zones

$($

A

$,$

$$B

$.$

$.$

$.$

$,$

$$F

$)$

$.$

$$Each delivery zone is served by a single e

$-$

bike. A preliminary analysis showed that one cargo e

$-$

bike has enough capacity to fulfill the daily demand of any given zone. The table below shows the

$($

X

$,$

$$Y

$)$

$$coordinates of the zone's centers and the area

$($

in squared Km

$)$

$$of each zone. Additionally, it gives information about the number of customers and the number of bottles of water ordered that will be attended on an average day.

Zone Coordinates

$($

X

$,$

Y

$)$

$($

km

$)$

$$Area

$($

Km

$2$

$)$

$$Number of customers Bottles ordered

A

$($

$7$

$,$

$1$

$0$

$)$

$0$

$.$

$6$

$1$

$7$

$0$

$8$

$4$

$0$

B

$($

$1$

$4$

$,$

$9$

$)$

$0$

$.$

$6$

$5$

$5$

$6$

$1$

$0$

$8$

$0$

C

$($

$2$

$2$

$,$

$8$

$)$

$0$

$.$

$5$

$7$

$7$

$2$

$6$

$4$

$8$

D

$($

$5$

$,$

$2$

$)$

$0$

$.$

$5$

$9$

$6$

$0$

$4$

$2$

$0$

E

$($

$1$

$3$

$,$

$1$

$)$

$0$

$.$

$5$

$1$

$5$

$9$

$8$

$8$

$8$

F

$($

$2$

$0$

$,$

$1$

$)$

$0$

$.$

$4$

$2$

$7$

$3$

$2$

$2$

$2$

Notice that the distribution center

$($

DC

$)$

$$is located at coordinates

$($

$0$

$,$

$0$

$)$

$.$

The accounting department has shared cost information from similar vehicles. Based on this information, Ruby Gonzalez estimated the following:

The cost to load each e

$-$

bike at the DC is $

$5$

$.$

The cost to stop at a customer location is $

$0$

$.$

$3$

$$per stop.

The cost to unload and deliver a single bottle of water at a destination is $

$0$

$.$

$0$

$1$

$.$

The cost for riding the e

$-$

bikes is $

$3$

$.$

$5$

$$per Km

$.$What is the daily cost for the linehaul riding of all the e$-$bikes from the DC to the center of each delivery zone and back $($roundtrip linehaul cost$)?$ Given the nearly perfect road network in downtown Tegucigalpa, estimate the linehaul distance based on L$1$ norm $($Manhattan distance$).$ This means you need to measure the distance between two points along axes $($X$,$ Y$)$ at right angles. Assume a linehaul circuity factor $()$of $1\mathrm{.}0505$