Su'aalo Tusaale ah oo Ka Hadlaya Adeegsiga Isku-dhafka ee Dhinaca Dhaqaalaha iyo Ganacsiga
Pendahuluan
Isku-dhafka waa fikrad muhiim ah oo ku jirta xisaabinta waxayna leedahay codsiyo badan oo dhinacyo kala duwan ah, oo ay ku jiraan dhaqaalaha iyo ganacsiga. Xaaladdan, isku-dhafka waxaa badanaa loo isticmaalaa in lagu falanqeeyo faa'iidada guud, kharashka, dakhliga, iyo isticmaalka iyo hawlaha wax soo saarka. Fahmidda isticmaalka isku-dhafka ah ee dhaqaalaha iyo ganacsiga ma aha oo kaliya inay caawiso xallinta dhibaatooyinka farsamada laakiin sidoo kale waxay bixisaa aragtiyo qoto dheer oo ku saabsan dhaqdhaqaaqa suuqa, go'aan qaadashada, iyo qorsheynta istaraatiijiyadeed.
Codsiyada Isku-dhafan ee Dhaqaalaha iyo Ganacsiga
1. Xisaabi Wadarta Dakhliga
Si loo xisaabiyo dakhliga guud, waxaan inta badan u baahanahay inaan isku darno dakhliga yar ee laga helo iibinta cutubyada shaqsiga ah ee badeecada. Haddii qiimaha badeecadu uu kala duwan yahay iyadoo ku xiran tirada la iibiyay, markaa shaqada qiimaha-tirada waa in la isku daraa si loo go'aamiyo wadarta dakhliga.
Tusaale ahaan dhibaatooyinka:
Ka soo qaad qiimaha \( p \) ee badeecaddu waxay ku xiran tahay tirada badeecada \( q \) la iibiyay, taas oo lagu bixiyo shaqada soo socota:
\[ p(q) = 100 – 2q \]
Xisaabi wadarta dakhliga haddii 10 cutub oo alaab ah la iibiyo.
Xalka:
Wadarta dakhliga \( R \) waa isku-dhafka qiimaha marka loo eego tirada u dhaxaysa cutubyada 0 ilaa \( Q \).
\[ R = \int_{0}^{Q} p(q) \, dq \]
Iyadoo \( p(q) = 100 – 2q \) iyo \( Q = 10 \):
\[ R = \int_{0}^{10} (100 – 2q) \, dq \]
Markaa, waxaan xisaabineynaa isku-dhafka:
\[ R = \left[ 100q – q^2 \right]_{0}^{10} \]
Qiimee xadka isku-dhafka ah:
\[ R = \left( 100 \cdot 10 - 10^2 \right) - \left( 100 \cdot 0 - 0^2 \right) \]
\[ = 1000 – 100 \]
\[ = 900 \]
Markaa, wadarta dakhliga haddii 10 cutub oo alaab ah la iibiyo waa 900.
2. Xisaabi Wadarta Kharashka
Isticmaalka isku-dhafka marka la xisaabinayo wadarta kharashyada wax soo saarka waa mid aad waxtar u leh, gaar ahaan marka kharashyada marginal aysan joogto ahayn oo ay ku xiran yihiin tirada la soo saaray. Kharashyada marginal waxaa lagu tilmaami karaa inay yihiin wax soo saarka kharashyada guud, iyo si loo helo wadarta kharashyada aan u baahanahay inaan isku darno.
Tusaale ahaan dhibaatooyinka:
Haddii kharashka yar ee lagu soo saarayo cutubyada \( q \) ee alaabta lagu bixiyo:
\[ MC(q) = 50 + 3q^2 \]
Xisaabi wadarta kharashka haddii 5 cutub oo alaab ah la soo saaro iyadoo la tixgelinayo kharashyo go'an \( C \) oo ah 200.
Xalka:
Wadarta kharashka \(TC \) waa isku-dhafka kharashka yar iyo kharashka go'an:
\[ TC = \int_{0}^{Q} MC(q) \, dq + C \]
Iyadoo \( MC(q) = 50 + 3q^2 \) iyo \( Q = 5 \):
\[ TC = \int_{0}^{5} (50 + 3q^2) \, dq + 200 \]
Waxaan xisaabineynaa isku-dhafka:
\[ TC = \left[ 50q + q^3 \right]_{0}^{5} + 200 \]
Qiimee xadka isku-dhafka ah:
\[ TC = \left( 50 \cdot 5 + 5^3 \right) – \left( 50 \cdot 0 + 0^3 \right) + 200 \]
\[ = \left( 250 + 125 \right) + 200 \]
\[ = 375 + 200 \]
\[ = 575 \]
Markaa, wadarta kharashka lagu soo saarayo 5 cutub oo alaab ah waa 575.
3. Xisaabinta Isticmaalka Kheyraadka
Isku-dhafka waxaa sidoo kale loo isticmaalaa in lagu xisaabiyo wadarta isticmaalka ama isticmaalka kheyraadka muddo cayiman. Tani waxay si gaar ah khuseysaa xaaladaha ganacsiga ee ku lug leh kheyraadka sida tamarta, agabka, ama dadka.
Tusaale ahaan dhibaatooyinka:
Heerka isticmaalka tamarta maalinlaha ah \( E \) ee warshadda wuxuu raacaa shaqadan soo socota ee jibbaaran:
\[ E(t) = 10e^{0.1t} \]
Xisaabi wadarta isticmaalka tamarta muddo 10 maalmood ah.
Xalka:
Wadarta isticmaalka tamarta \(C \) muddada [0, T] waa isku-dhafka heerarka isticmaalka tamarta:
\[ C = \int_{0}^{T} E(t) \, dt \]
Iyadoo \( E(t) = 10e^{0.1t} \) iyo \( T = 10 \):
\[ C = \int_{0}^{10} 10e^{0.1t} \, dt \]
Si loo xisaabiyo isku-dhafka, waxaan isticmaali karnaa farsamada beddelka ah:
U ogolow \( u = 0.1t \), ka dibna \( du = 0.1 \, dt \), ama \( dt = \frac{du}{0.1} \),
\[ C = \int_{0}^{1} 10e^{u} \frac{du}{0.1} \]
\[ = 100 \int_{0}^{1} e^{u} \, du \]
\[ = 100 \left[ e^{u} \right]_{0}^{1} \]
Qiimee xadka isku-dhafka ah:
\[ C = 100 \bidix( e^{1} – e^{0} \midig) \]
\[ = 100 \bidix(e – 1 \midig) \]
Iyadoo \( e \qiyaastii 2.718 \):
\[ C \qiyaastii 100 (2.718 – 1) \]
\[ = 100 \jeer 1.718 \]
\[ = 171.8 \]
Markaa, wadarta isticmaalka tamarta ee 10 maalmood waa 171.8 unug oo tamar ah.
Gabagabo
Fikradda isku-dhafka ah waa mid muhiim u ah dhaqaalaha iyo ganacsiga, maadaama ay u oggolaanayso falanqeeyayaasha iyo go'aan-qaatayaasha inay xisaabiyaan oo saadaaliyaan isbeddellada muhiimka ah sida dakhliga, kharashyada, iyo isticmaalka. Fahmidda sida loo isticmaalo isku-dhafka ah xaaladahan kala duwan waxay bixin kartaa faa'iido tartan iyo aragti wanaagsan oo ku saabsan hawlaha ganacsiga. Waxaan rajeyneynaa, dhibaatooyinkan tusaalaha ah waxay kaa caawin doonaan inaad fahamto codsiyada wax ku oolka ah ee isku-dhafka ah ee dhaqaalaha iyo ganacsiga.
