I need the solution of this problem, its really important, please help me with this.

A logistics operator needs to find the best location for a distribution center that is equidistant from the delivery points for a distribution network in Colombia. However, you have to keep in mind that there are some cities that have a higher volume of orders and for this reason, it is necessary to prefer attention to those points with more profitable clients than other points of delivery. The Director of Logistics Operations of the company must suggest a possible location and present the results to the steering committee. You must convince the members of said committee that this proposal will improve the profitability of the network and in turn give more preference to more of the company (type A customers). The Director of Operations asks the transport area for data about the latest deliveries and the area in charge provides you with the following:

Delivery Point	Logistics cost / Volumetric weight	Number of boxes delivered	Type of box	Product family
Apartad	140	34503	2	Body Care
Armenia	90	83990	2	Beauty Care
Barbosa	100	864	3	Beauty Care
Barrancabermeja	50	83945	2	Oral Care
Barranquilla	200	506851	2	Body Care
Baranoa	100	120640	2	Body Care
Bello	190	45306	3	Oral Care
Bogot	50	913078	1	Beauty Care
Bucaramanga	190	685690	1	Oral Care
Buga	70	21811	2	Oral Care
Bugalagrande	160	1156	2	Body Care
Caicedonia	50	3937	1	Oral Care
Cali	40	1204565	2	Oral Care
Cartagena	180	248157	3	Body Care
Cartago	20	27116	3	Oral Care
Chinchin	30	10091	3	Oral Care
Cota	90	98657	1	Beauty Care
Ccuta	70	91585	1	Beauty Care
Dosquebradas	90	56230	2	Beauty Care
Duitama	180	156481	2	Oral Care
El Cerrito	170	5226	1	Body Care
El Zarzal	20	1217	2	Beauty Care
Envigado	130	2778	1	Body Care
Espinal	70	7264	2	Body Care
Facatativ	20	21431	1	Oral Care
Florencia	60	10693	3	Body Care
Florida_Valle	90	14731	3	Beauty Care
Floridablanca	60	33914	1	Beauty Care
Funza	40	2067062	3	Body Care
Fusagasug	130	40311	2	Body Care
Girardot	100	1432	1	Body Care
Girn	70	11725	1	Body Care
Ibagu	60	271458	1	Beauty Care
Itag	160	314208	2	Beauty Care
Jamund	20	9337	3	Oral Care
La Tebaida	140	855	3	Body Care
Manizales	70	48655	2	Body Care
Medelln	160	869206	2	Body Care
Melgar	200	2336	2	Beauty Care
Montera	170	308772	2	Oral Care
Mosquera	80	133831	2	Body Care
Neiva	30	195042	2	Beauty Care
Nemocn	70	2941	3	Beauty Care
Palmira	110	40298	3	Oral Care
Pasto	100	209632	3	Beauty Care
Perira	200	261648	3	Beauty Care
Pi de Cuesta	200	28549	2	Beauty Care
Popayn	70	1026	3	Oral Care
Rio Negro	110	847	3	Beauty Care
Sabana de Torres	150	1020	3	Beauty Care
Sabaneta	170	24793	3	Body Care
San Alberto	180	800	2	Body Care
San Andrs	100	17924	2	Beauty Care
San Gil	170	983	1	Beauty Care
San Pablo Bolvar	150	1238	1	Body Care
Santa Marta	200	67278	1	Body Care
Santa Rosa de Cabal	90	5702	1	Oral Care
Santander de Quilichao	190	5936	3	Oral Care
Sincelejo	100	50880	1	Beauty Care
Socorro	170	255	1	Oral Care
Sogamoso	190	20984	3	Beauty Care
Soledad	20	156520	2	Beauty Care
Tocaima	150	536	2	Body Care
Tulu	130	70163	3	Oral Care
Tunja	40	30167	1	Oral Care
Valledupar	140	90521	2	Beauty Care
Villavicencio	70	272066	2	Body Care
Yumbo	40	32834	2	Oral Care

Additionally, there is other information from the area of operations regarding requirements of company logistics:

Type of boxes	Dimensions (cm)	Maximun weight (kg)
Type 1	33,0x22,0x31,0	6,5
Type 2	36,0x24,0x27,0	7,2
Type 3	37,5x25,0x30,5	7,8

The volumetric weight, in order to apply the rates and calculate the weight-volume relationship of the boxes, is calculates as follows:

Volumetric weight = Volume(m³) x 250 (m³/kg)

The marketing area provides the following information regarding the sale price of each product family (estimated for each milliliter of product):

Product Family	Selling price per milliliter of product
Beauty Care	$2,50
Oral Care	$0,59
Body Care	$0,74

The projects area affirms that there is the feasibility of choosing between these possible locations: Ibagu, Envigado, Funza, Floridablanca, since building a distribution center has another type of macroeconomic considerations, obtaining qualified labor, access to vehicles load, among other criteria.

Company operations to respond: 1. If the criteria is minimum cost, what would be the most economical location? 2. If the criterion is to maximize the Profit vs. Cost, what would this location be?