M'ndandanda wazopezekamo[Bisani][Show]
Makampani omwe amasangalatsa kwambiri omwe akufunafuna ntchito ndi malonda a ndalama. Mabizinesi apakompyuta amalandila zopempha kuchokera kwa amalonda padziko lonse lapansi kuti apereke nsanja yogulitsira yomwe imatha kuwunika mwachangu komanso moyenera deta yophatikizira ndalama.
Pulatifomu yamalonda ndi pulogalamu yamapulogalamu yoperekedwa kwa amalonda ndi osunga ndalama ndi mabungwe ena azachuma, monga mabanki, ndi mabanki.
Mapulatifomu amalonda amalola osunga ndalama ndi ogulitsa kuyika mabizinesi ndikuyang'anitsitsa maakaunti awo. Ntchito zina zomwe zimathandiza osunga ndalama popanga zisankho zamabizinesi nthawi zambiri zimaphatikizidwa muzamalonda.
Zolemba zenizeni zenizeni, ma chart ochezera, zida zosiyanasiyana zojambulira, ma feed a nkhani zamoyo, ndi kafukufuku wamtengo wapatali ndi zitsanzo zochepa za kuthekera uku.
Mapulatifomu amathanso kupangidwira misika ina, monga ya masheya, ndalama, zosankha, kapena zam'tsogolo.
Kwa zaka zopitirira khumi, machitidwe opangira malonda, omwe amadziwikanso kuti malonda a algorithmic, atenga gawo lapakati pazamalonda.
"Njira yamalonda," yomwe nthawi zina imadziwika kuti "ndondomeko yamalonda," sichinthu chongowonjezera malamulo omwe amagwiritsidwa ntchito pazomwe amalowetsamo kuti apereke kugula / kugulitsa zolowera ndi kutuluka. Ngakhale kuti kupanga njira yamalonda kungawoneke kosavuta, sichoncho!
Malingaliro omwe amatsata njira yogulitsira yochulukira amatchedwa "Quants" m'dera la malonda a algorithmic popeza kupanga njira yabwino yogulitsira kumafuna kuphunzira mozama.
Mapangidwe ofunikira a makina opangira malonda asintha kwambiri pazaka khumi zapitazi ndipo akusinthabe.
Bizinesi yamalonda ya algorithmic yakhala poyambira pazachitukuko chaukadaulo wamakompyuta ndi maukonde chifukwa kwakhala kofunikira kuti mabizinesi, makamaka omwe amagwiritsa ntchito njira zogulitsira zothamanga kwambiri, apangitse luso laukadaulo kuti apikisane nawo pazamalonda a algorithmic.
Tikambirana za nsanja yamalonda dongosolo dongosolo m'nkhaniyi. Zomwe zimafunikira papulatifomu yamalonda zimaphatikizapo kapangidwe kake, ma protocol, ndi malangizo opangira makina anu ochitira malonda.
Zofunikira zamapulogalamu ochita malonda pamlingo woyambira
Yankho labwino kwambiri ndi lomwe limakwaniritsa zofunikira zamapulogalamu. Mfundo zazikuluzikulu zomwe mapulogalamu ochita malonda odzichitira okha ndi awa:
- Scalability (kuthekera kwadongosolo kuthana ndi kuchuluka kwa zopempha ndi kuchuluka kwa ntchito);
- Multiprocessing ndi ntchito yabwino;
- Chitetezo ndi chitetezo (momwe zimachitikira kuphwanya kapena kumenyedwa komwe kumabwera mwadzidzidzi ndikuteteza kulowa mosaloledwa);
- Kugwirizana (kuthekera kwa dongosolo lolumikizana ndi machitidwe ena);
- Kudalirika (momwe umathetsera zolephera ndikuyendetsa ngakhale zovuta).
Machitidwe ochita malonda a algorithmic amafunikira antchito aluso kwambiri komanso kusamalitsa. Ndikosavuta kumvetsetsa zofunikira za dongosololi ngati pali zofunikira zosagwira ntchito. Amagwira ntchito ngati miyezo yoyendetsera magulu opanga mapulogalamu kuti akhazikitse ndikutanthauzira mtundu wa chinthu.
Zochita za nsanja zamalonda zimaphatikizapo
Thandizo lopambana la njira zosiyanasiyana zolipirira, mautumiki otetezedwa amtambo, zida zamphamvu zowunikira deta, kuwongolera zoopsa, mawu omveka bwino, ndi mitundu yoyenera yamatchati ndizofunikira zonse zofunikira.
Zotsatirazi ndi zina mwazofunikira zamapulatifomu opangira okha omwe amalonda onse amawasamalira:
Dashboard yowonetsa ziwerengero
Pofuna kuyesa zenizeni zenizeni, kuwunika kwanthawi imodzi kwamitengo yandalama m'magawo angapo anthawi, nsanja iyenera kuyendetsa zosintha mosalekeza, kugwiritsa ntchito deta kuchokera kumatchati ambiri, ndikugwiritsa ntchito mapepala amitengo.
kutsimikizika
Njira yotsimikizira mwachangu koma yodalirika imapanga chithunzi cha nsanja yotetezeka komanso kuyesetsa kwaukadaulo wapamwamba.
Mapulogalamu ogulitsa amatha kuthandizira kupeza kuchokera kumaakaunti angapo, ofanana ndi nsanja zamalonda zotseguka zokhala ndi kutsimikizika kwazinthu ziwiri (pogwiritsa ntchito SMS kapena Google Authenticator, mwachitsanzo), koma muthanso kukhala ndi dongosolo lokhala ndi mwayi wopezeka kudzera pa imelo, nambala yafoni, kapena zina. njira za gulu laling'ono chabe la amalonda.
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Musanapange zisankho zilizonse zachuma, ndikofunikira kuti mupange kafukufuku wanu. Pofuna kupewa zolakwika zomwe zimadza chifukwa cha umbuli, amalonda angapindule ndi nkhani zosavuta, zowonetseratu zoyenera, ndi zidziwitso za msika wa ndalama zapadziko lonse lapansi, zomwe zimapezeka nthawi yomweyo pamapulatifomu awo ogulitsa.
Kugwira ntchito kwa ma admins ndi ogwiritsa ntchito ndikosavuta
M'dongosolo loterolo, kuthekera koyendetsa zonse mwachangu ndikudina kamodzi ndikofunikira. Izi zikuphatikizapo kuyang'anira zochitika, maoda omwe akuyembekezera ndi kutumizidwa, maakaunti anu, ziwonetsero za madongosolo, ndi zopempha zamakasitomala.
Izi zimathandizira kupanga zisankho munthawi yochepa kwambiri komanso zimatsimikizira kupezeka kwa chidziwitso chofunikira mosalekeza.
Kugwiritsa ntchito zidziwitso zokankhira
Ogwiritsa ntchito akuyembekeza kuti nsanja zamalonda zizipezeka usana ndi usiku ndipo azidziwitsidwa zachitetezo chilichonse kapena zosintha zaposachedwa.
Mutha kudziwa zambiri ndi zidziwitso zomwe mungasinthire makonda pomwe nsanja yamalonda imatsata zochitika zachuma, kusinthasintha kwamitengo, chitukuko cha msika, zizindikiro zaukadaulo, ndi zina zambiri, ndikutumiza zosintha zamalo anu.
Kutulutsa ndalama ndi malipiro
Izi ndizofunikira kuti muthe kuchita malonda, kuyang'anira kayendetsedwe ka ndalama, ndikuchotsa ndalama mwachangu muakaunti yanu pogwiritsa ntchito kirediti kadi, PayPal, kapena kusamutsa ku banki molunjika.
Pempho lanu lochotsa likamaliza kukonzedwa, mudzadziwitsidwa.
Kamangidwe ka Automated Trading System
Injini yomwe imapanga zisankho papulatifomu yochitira malonda, yomwe imadziwikanso kuti injini ya 'Complex Event Processing', kapena CEP, idzakhala mkati mwa pulogalamu ya seva.
The Application layer kwenikweni ndi a mawonekedwe a mawonekedwe kuyang'anira ndi kupereka magawo ku CEP. Ngakhale kuti gawo la pulogalamuyo ndi mawonekedwe, zowunikira zina (zomwe tsopano zakhala zikusowa mphamvu chifukwa cha vuto la kukula) zitha kutsitsidwa pagawo la pulogalamuyo, makamaka zomwe zimakhudzana ndi kuwongolera kwazomwe ogwiritsa ntchito monga zolakwika zala zamafuta.
Mkhalidwe wochititsa chidwi umachokera ku vuto la scalability mu makina ochita malonda.
Tiyerekeze kuti chochitika chimodzi chamsika chikukonzedwa ndi malingaliro 100 (monga tafotokozera m'chitsanzo choyambirira). Pamagawo ambiri amalingaliro 100, tinene kuwerengera kwa Agiriki pazosankha, patha kukhala zigawo zofananira zamawerengedwe ovuta omwe ayenera kuchitidwa.
Kuwerengera kofananako kukanachitidwa ndi gawo lililonse ngati lingaliro lililonse lizigwira ntchito palokha, zomwe zingawononge zopangira.
Kuwerengera kovutirapo komwe kumagawika nthawi zambiri kumagawidwa m'mainjini osiyanasiyana owerengera omwe amapereka ma Greek monga chothandizira ku CEP munjira yochitira malonda yodzichitira kuti achulukitse kuchulukirachulukira.
Pakadali pano, Risk Management System (RMS) yosiyana mkati mwa Order Manager (OM) imawunika zotsalazo pamakina ochita malonda atangotsala pang'ono kutulutsa lamulo.
Popeza pali dongosolo limodzi lokha la RMS loyang'anira chiwopsezo pamagulu onse / njira zomveka, m'mbuyomu, amalonda 100 osiyana anali kuwongolera chiwopsezo chawo. Izi ndichifukwa cha vuto la sikelo.
Komabe, kuwunika kwina kwachiwopsezo kumatha kukhala kwa njira zinazake, pomwe ena angafunikire kuchitidwa m'njira zonse.
Chifukwa chake, RMS yokha imakhala ndi RMS yapadziko lonse (GRMS) ndi strategy level RMS (SLRMS). SLRMS ndi GRMS zitha kuwonedwanso kudzera pa mawonekedwe ogwiritsa ntchito (UI).
Tiyeni tsopano tipite patsogolo pazigawo za seva.
Adapter ya Msika
Kusinthana kapena wina aliyense wopereka zidziwitso zamsika amatumiza deta mumtundu wake. Chilankhulo chimenecho chikhoza kumveka kapena sichingamveke ndi dongosolo lanu lamalonda la algorithmic.
Kusinthana kumakupatsani mwayi wopeza API (Chiyankhulo Chopanga Ntchito) chomwe mungagwiritse ntchito popanga adaputala yanu kuti musinthe mtundu wa data kukhala mtundu womwe dongosolo lanu lingamvetse.
Complex Event Processing Engine
Ubongo wa njira yanu uli mu gawo ili. Mukakhala ndi deta, muyenera kuigwiritsa ntchito molingana ndi dongosolo lanu, lomwe limafuna kuti muzichita mawerengedwe osiyanasiyana, kujambula mafananidwe ndi deta yakale, ndikupanga zisankho zomwe zidzatsogolera kupanga malamulo.
Chida ichi chimapangidwa pogwiritsa ntchito mtundu wa dongosolo ndi kuchuluka kwa dongosolo. Mwachidule, chochitika chovuta ndi mndandanda wa zochitika zomwe zikubwera. Izi zimakhala ndi nkhani, mayendedwe amsika, machitidwe amsika, ndi zina.
Kumaliza ntchito zamakompyuta pazochitika zovuta mwachangu kumadziwika ngati kukonza zochitika zovuta. Zochita zamakina ochita malonda zitha kuphatikizira kuwona machitidwe ocholoka, kupanga maulalo, ndikukhazikitsa kulumikizana monga chifukwa ndi nthawi pakati pa chidziwitso chilichonse chomwe chikubwera.
Order Routing System
Pogwiritsa ntchito ma API omwe aperekedwa, dongosololi limasungidwa m'chinenero chomwe kusinthaku kungamvetse. Kusinthanitsa kumapereka ma API achilengedwe ndi FIX APIs, mitundu iwiri yosiyana ya ma API.
Native APIs adapangidwa kuti azisinthana. Ndondomeko zotsogola zomwe zimadziwika kuti FIX (Financial Information Exchange) zimagwiritsidwa ntchito ndi masinthidwe angapo kuti atsogolere ndikuwongolera kayendedwe ka data m'misika yachitetezo.
Mu gawo lotsatirali, tifotokoza zambiri za FIX. Ngati chuma chili chotseguka, anthu atha kutumiza maoda kudzera munjira yochitira malonda okha kusinthanitsa kapena kusasinthana, ndipo ORP ikuyenera kuyang'anira maoda opita mbali zambiri.
Pano, tikufuna kutsindika kuti chizindikiro cha dongosolo chikhoza kuchitidwa pamanja ndi munthu kapena basi. Gawo lomaliza ndi lomwe timatcha "njira yochitira malonda yodzichitira yokha."
Ma module oyang'anira madongosolo amaphatikizapo njira zingapo zochitira zomwe zimatsata kugula / kugulitsa malinga ndi malingaliro omwe adakhazikitsidwa kale.
chiopsezo Management
Popeza njira zopangira malonda zimagwira ntchito popanda kukhudzidwa ndi anthu, kuwunika kowopsa ndikofunikira kuti zitsimikizire kuti machitidwe azamalonda akugwira ntchito momwe amafunira.
Kusawongolera bwino kwachiwopsezo kapena kusowa kwa macheke kumakampani ochulukirachulukira kungabweretse zotayika zazikulu zomwe sizingabwezedwe. Zotsatira zake, makina aliwonse ochita malonda ayenera kukhala ndi dongosolo loyang'anira ngozi (RMS).
Kupititsa patsogolo kwa ma protocol a makina ochita malonda
Kuti mugwirizane ndi malo angapo kuchokera ku seva imodzi, zomwe zinatheka chifukwa cha luso la zomangamanga kuti lifike ku njira zambiri pa seva, zinkafunika.
Kutumiza ma oda kumalo angapo ndikulandila zambiri kuchokera kumisika yambiri, woyang'anira dongosolo, motero, adayika ma adapter angapo.
Ntchito ya adaputala iliyonse ndikukhala womasulira pakati pa njira yolumikizirana mkati mwa dongosolo ndi protocol yomwe kusinthana kumamvetsetsa. Chifukwa chake, pamafunika ma adapter angapo kuti asinthane.
Popeza kusinthanitsa kulikonse kuli ndi ndondomeko yogwirizana ndi zomwe zimapereka, adaputala yatsopano iyenera kupangidwa ndikumangidwira muzomangamanga kuti iwonjezere kusinthana kwatsopano ku machitidwe opangira malonda.
Ma protocol okhazikika apangidwa kuti ateteze mutu uwu wa kuyika kwa adaputala. Protocol ya FIX ndiyodziwika kwambiri mwa onse.
Nthawi yopita kumsika yolumikizana ndi malo atsopano imafupikitsidwa kwambiri, zomwe sizimangopangitsa kuti zizitha kulumikizana ndi malo angapo poyenda.
Dongosolo lochita malonda lodzichitira nokha limatha kuyanjana mosavuta ndi ena ogulitsa pazowunikira kapena ma data amsika chifukwa cha kukhalapo kwa ma protocol wamba.
Zotsatira zake, msika umakhala wopambana kwambiri chifukwa palibenso choletsa kuphatikiza ndi malo atsopano kapena wogulitsa.
Kuonjezera apo, kuyerekezera kumapangidwa mophweka kwambiri chifukwa zonse zomwe zimafunika kuti zigwirizane ndi simulator pogwiritsa ntchito FIX protocol ndikupereka madongosolo ndi kulandira deta kuchokera kumsika weniweni.
Simulator yokha imatha kupangidwa mkati kapena kugulidwa kuchokera kuzinthu zina. Zofanana ndi zomwe zili pamsika, ma data ojambulidwa amathanso kubwerezedwanso chifukwa cha ma adapter osatengera zomwe zachokera.
Zomangamanga zotsika latency zomwe zikubwera
Njirazi tsopano zitha kuwunika kuchuluka kwa data munthawi yeniyeni ndikupanga zisankho zachangu zamalonda chifukwa cha zoyambira zamakina ochita malonda.
Chifukwa cha chitukuko cha njira zoyankhulirana zamakampani monga FIX, tsopano ndizosavuta kupanga desiki yamalonda ya algorithmic kapena makina ochita malonda, omwe achulukitsa mpikisano pamsika wamalonda wa algorithmic.
Kugogomezerako kudasinthiratu kutsitsa latency popanga zisankho pomwe ma seva amakumbukira kwambiri komanso mawotchi othamanga.
Kuchepetsa latency kwakhala kofunikira pakapita nthawi pazifukwa zosiyanasiyana, kuphatikiza:
- Pokhapokha pa malo otsika a latency pamene njirayo imakhala yomveka.
- Mpikisano umakuchotsani ngati simunafulumire mokwanira kuti mupulumuke masewera olimbitsa thupi
Colocation yakhala yofunika kwambiri pamakina opangira malonda panjira iliyonse yothamanga kwambiri yokhudzana ndi komwe mukupita.
Koma machitidwe osiyanasiyana amafunikira kukonzekera bwino. Asanapange chisankho chotere, munthu ayenera kuganizira zosintha monga kutalika kwa nthawi yoyankhira madongosolo a komwe akupita komanso momwe ikufananira ndi nthawi ya ping pakati pa malo awiriwa.
Kuti muchepetse kuchuluka kwa latency ya makina opangira malonda, network latency nthawi zambiri ndiye chinthu choyamba kuwongolera. Koma kamangidwe kakhoza kukonzedwanso m’njira zina zambiri.
Network Processing Latency
Network processing latency ndi kuchedwa kumene ma routers, masiwichi, ndi zina zotero. Chiwerengero cha ma hop chomwe chimatengera kuti paketi isunthe kuchokera ku point A kupita ku B ingakhale gawo lotsatira la kukhathamiritsa popanga makina opangira malonda.
Kudumphira kumafotokozedwa ngati gawo la njira pakati pa gwero la paketi ndi kopita komwe sikudutsa pa chipangizo chakuthupi, monga rauta kapena switch.
Zomwe timatcha ma microbursts zitha kukhalanso ndi chiwopsezo pakuchedwa kwa ma network.
Kuthamanga kwachangu pamayendedwe otumizira deta komwe kungakhudze kapena kusakhudza kuchuluka kwa kusamutsa deta kumatchedwa microburst.
Popeza machitidwe opangira malonda amatengera malamulo, onse amayankha mofanana pazochitika zomwezo. Kusamutsa kwa data pang'ono pakati pa omwe akutenga nawo mbali ndi komwe akupita kumatha kuchitika chifukwa cha machitidwe angapo omwe akutenga nawo mbali kutumiza malamulo nthawi imodzi.
Kugwiritsa ntchito latency
Kuchedwa kwa ntchito kwa makina ochita malonda ndi muyeso wa nthawi yomwe zimatengera kukonza ntchito. Izi zimatengera kuchuluka kwa mapaketi, kukonzedwa komwe kumaperekedwa kumalingaliro ogwiritsira ntchito, zovuta za mawerengedwe omwe amagwiritsidwa ntchito, magwiridwe antchito, ndi zina zambiri.
Dongosololi lingakhale ndi kuchedwetsa kocheperako pamene purosesa yake ikuchulukirachulukira. Ndi mawotchi apamwamba kwambiri, zomwezo zimakhalanso zoona.
Makina ambiri ochita malonda amapindula pogawa ma CPU kumadera ovuta kwambiri a pulogalamuyi, monga malingaliro amalingaliro, mwachitsanzo. Pochita izi, ndondomekoyi sikuwonjezera kuchedwa komwe kumabwera chifukwa chosintha ma cores.
Zofanana ndi izi, ngati njira yochitira malonda yodzichitira yokha idakonzedwa ndi kukula kwa cache ndi kuyandikira kwa kukumbukira kukumbukira, pangakhale kugunda kwa kukumbukira kangapo, kumachepetsanso kuchedwa.
Machitidwe ambiri amachita izi mwa kukhathamiritsa kachidindo kamangidwe ka purosesa, zomwe zimachitika pogwiritsa ntchito zilankhulo zotsika kwambiri.
Pogwiritsa ntchito zipata zokonzekera bwino, mabizinesi ena afika mpaka pakuwotcha ma computations ovuta pa hardware (FPGA).
kuyezetsa
Kuyesa, komwe ndi kuzindikiritsa zolakwika za pulogalamu ya pulogalamu, sikutheka kunyalanyazidwa, makamaka ku Fintech. Chifukwa cha kuthekera kwa kutayika kwachuma, luso lazachuma silingakwanitse kukhala ndi zolakwika.
Kuchuluka kwa zolakwika zomwe akatswiri otsimikizira zaubwino angazindikire, m'pamenenso m'pamenenso kuti chomalizacho chizigwira ntchito moyenera. Kutengera ndi kampani yomwe ikupanga nsanja yamalonda kapena zosowa za kasitomala, njira yoyeserera imaphatikizapo:
Maziko a kuyesa kogwira ntchito ndikupanga zolowera ndikusanthula zotsatira. Pogwiritsa ntchito makhadi onama, milandu yoyesa ntchito zachuma imayendetsedwa. Makhadiwa amafuna kuwongolera kudalirika, kuchita bwino, ndi kulondola kwa malipiro.
Kupeza liwiro la dongosolo, scalability, ndi kukhazikika kumachitika kudzera pakuyesa magwiridwe antchito. Kuthamanga kwa pulogalamuyo kumawunikidwa kuti amvetsetse momwe imayankhira mwachangu, ndipo kuchuluka kwake kumawonetsa kuchuluka kwa ogwiritsa ntchito omwe angathandizire nthawi imodzi popanda kugwa.
Kuonjezera apo, kukhazikika kumasonyeza ngati ntchitoyo ikugwira ntchito moyenera pansi pa katundu wosiyanasiyana kapena ngati pali zolakwika zina.
Zitha kukhala zopitirira mphamvu za wogulitsa malonda m'modzi kuti apange dongosolo lazamalonda lokhazikika. Machitidwe opangira malonda, omwe amaperekedwa m'misika polembetsa, ndi mwayi kwa amalonda omwe akufuna kufufuza njira ya algorithmic ya malonda.
Kupanga Machitidwe Anu Anu Ochita Kugulitsa
Ogulitsa ongoyamba kumene amatha kupanga njira zawo zogulitsira za algorithmic ndikuchita nawo malonda opambana amsika. Monga chidule chambiri, magawo omwe alembedwa pansipa atha kugwiritsidwa ntchito kupanga njira yamalonda ya algorithmic:
- Pangani lingaliro lamalonda lomwe mukuganiza kuti lingakhale lopambana m'misika yogwira ntchito pogwiritsa ntchito malingaliro anu kapena njira. Lingaliroli litha kutengedwa kuchokera kuzomwe mukuwona pamsika, mabuku ogulitsa, mapepala amaphunziro, mabulogu ogulitsa, mabwalo azamalonda, kapena gwero lina lililonse.
- Sonkhanitsani zofunikira - Mudzafunika mbiri yakale kuti muyese malingaliro anu. Izi zimapezeka kuchokera kwa ogulitsa data omwe amalipidwa kapena masamba ngati Google Finance.
- Kulemba dongosolo kumafuna kugwiritsa ntchito zida monga Excel, Python, kapena R mapulogalamu. Mukakhala ndi deta, mukhoza kuyamba kukopera njira yanu.
- Kuyesa lingaliro lanu lazamalonda motsutsana ndi mbiri yakale itatha kulembedwa kumatchedwa backtesting njira yanu. Kubwerera kumbuyo kumaphatikizapo kukhathamiritsa kwa zolowetsa, kukhazikitsa zolinga za phindu ndi kuyitanitsa kuyimitsa, kukula kwa malo, ndi ntchito zina zofananira.
- Pepala kugulitsa njira yanu - Kutsatira gawo lakumbuyo, kugulitsa mapepala njira yanu ndikofunikira. Izi ziphatikizapo kuyesa dongosolo lanu pogwiritsa ntchito makina oyerekeza ndi msika. Panjira yogulitsa mapepala, pali ma broker omwe amapereka nsanja yamalonda ya algorithmic.
- Ngati njira yanu ili yopindulitsa mutagulitsa mapepala, mutha kuyigwiritsa ntchito munthawi yeniyeni. Mutha kupanga akaunti yogulitsa ndi broker wodalirika yemwe amapereka malonda a algorithmic.
Chaka chilichonse, pamakhala kusinthana kochulukira komwe kumalola malonda a algorithmic kwa onse ochita malonda ndi ogulitsa, ndipo ochita malonda ochulukirachulukira akugwiritsa ntchito malonda a algorithmic.
Kutsiliza
Imeneyi inali nkhani yokwanira yomanga makina opangira malonda omwe tili ndi chidaliro kuti adapereka kumvetsetsa kwanzeru kwa zigawo zomwe zikukhudzidwa komanso zopinga zambiri zomwe opanga zomangamanga ayenera kuthana nazo / kugonjetsa kuti apange njira yolimba yopangira malonda.
Ndidachita zomwe ndingathe kuti ndikuwonetseni mwachidule machitidwe azamalonda, koma pali zambiri zomwe zikuchitika pansi pa hood. Ndikukhulupirira kuti mwapeza kuti nkhaniyi ndi yothandiza ndikuigwiritsa ntchito bwino.
Siyani Mumakonda